Ppe - Inhouse 3

 

PROBLEMS AND SOLUTIONS 1) A boiler fuel fuel contains contains 86.1% carbon, carbon, 12.5% hydrogen, hydrogen, 0.4% oxygen oxygen and 1% sulp sulphur. hur. 40% excess excess air is supplied supplied to the furnace and the fuel rate is 400 kg/h. Calcul Calculate ate the quantity quantity of heat energy transferred to the air per hour if it enters the air heater at 18C and leaves at 130°C. Take Cp for air  as 1.005 kJ/kgK and humidity ratio of 0.013kgv/kgda a. 904,200 kJ/hr b. 913736kJ/hr  c. 865425kJ/hr d. 758425kJ/hr 

Solution: QAPH = ma Cpa (Δt)air 2)

where: ma = (A/F”) mf

thus, QAPH = 913736 kJ/hr 

The constit constituent uentss of a fuel are 85% carbon, carbon, 13% hydrogen, hydrogen, and 2% oxygen. oxygen. When burning burning this this fuel in a boiler furnace furnace the air supply is 50% in excess of the theoretical theoretical minimum minimum required required for  complete combustion, complete combustion, the inlet temperatu temperature re of the air being 31°C and exit gas temperatur temperaturee of  280°C. Calculate the heat energy carried away to waste in the flue gases expressed as a percentage of the heat energy supplied, taking the specific heat of the flue gases as 1.005 kJ/kgK.   a. 10.85% b. 9.62% c. 15.63% d. 11.84% Solution: % Wh = {

  Qwh }(100%) mf HHV 

where: HHV = 14600C + 62000 (H – O/8) ;

Qwh/mf  =  = ( mfg/mf   ))  Cpfg Δtfg ; mfg/mf  = A/F + 1

thus, %Wh = 11.84%

3) In an experiment experiment to determine determine the calorific calorific value value of an oil fuel by means of a bomb calorim calorimeter, eter, the mass of the sample of fuel was 0.75 gram, mass of water surrounding the bomb 1.8 kg, water  equivalent of bomb and fittings 470 grams, and the rise in temperature was 3.3°C. Calculate the calorific value of this oil in MJ/kg. Take specific heat of water= 4.2 kJ/kgK.   a. 41.94MJ/kg  b. 32.15MJ/kg c. 25.63MJ/kg d. 65.63MJ/kg Solution: HHV = QF / msample 

where: QF = mwt Cpw Δtw 

thus, HHV = 41.94 MJ/kg

4) The mass analysi analysiss of a fuel is 84% 84% carbon, carbon, 14% hydrogen hydrogen and 2% ash. It It is burnt burnt with 20% excess excess air relative to stoichiometric requirement. requirement. If 100 kg/h of this fuel is burnt in a boiler determine the volumetric flow rate of the gas if its temperature and pressure are 250°C and 1 bar respectively.  Note: Air contains 23.1% oxygen by mass. R o= 8.3143 kJ/kg mol K and atomic mass relationships are: oxygen 16, carbon 12, hydrogen 1. a. 2569m3/hr b. 2759m3/h c. 1256m3/hr d. 5689m3/hr  Solution: Vfg = (mfg R fg fg Tfg)/Pfg R fg fg =

 R mw =0.28872

where: mfg/mf = 18.65 mfg=1827.73 kg/hr ;

 ;

Thus, Vfg = 2759.88 m3/hr. 5)

Steam Steam at 30 bar, 375°C, 375°C, is gene generat rated ed in a boiler boiler at the the rate of 30000 30000 kg/h from from feed water water at 130°C. The fuel has a calorific value of 42 MJ/kg and the daily consumption is 53 tonne. Calculate the equivalent engine power if the overall efficiency of the plant is 0.13.

 

a. 3349kW

 b. 2546kW

c. 5634kW

d. 8954kW

Solution: Po = (e plant) (mf  HHV) where: e plant = (Po/Pi) 100% ; e bo = ms(hs-hf ) /mf (HHV) thus, Po = 3349 kW 6) The equivalent equivalent evaporation evaporation of a boiler, boiler, from and and at 100C, is 15kgsteam/k 15kgsteam/kg g fuel, and the calorifi calorificc value of the fuel burned is 41.9MJ/kg. Find the efficiency of the b boiler. oiler. a. 82.8% b. 78.9% c. 85.6% d. 80.8% Solution: e bo = ms(hs-hf ) /mf (HHV) = (ese)(2257) / HHV

thus, e bo = 80.8%

7) An econo economi mize zerr receiv receives es hot gas gas (c p=0.27Btu/lb-R) and water in the ratio 1.56lbg/lbw. The gas enters at 850F and leaves at 355F; tthe he water enters at 120F. Find the exit temperature of the water  and the LMTD for parallel flow. a. 420.5F, 268F b. 320.5F, 228F  b. 365.8F, 321F c. 287.3F. 310F

Solution: LMTD   thus, t b = 320.5 °F mCpΔt =] gas = mCpΔt  ] water θmax – θmin / ln (θmax/θmin) thus, LMTD = 227.92°F 8)

St Stea eam m at 285ps 285psia ia ( tsat tsat=4 =413F 13F,, h g=1202.45Btu/lb) enters a convective superheater in a saturated state and leaves at 600F(h=1316.4). The hot gas (c p=0.241B =0.241Btu/lb tu/lb-F) -F) leave the superheater superheater at 1150F. There are 1.6 lbg/lbsteam and the total steam flow is 17,580lb/hr. If the transmittance is U=4Btu/hr-ft2-F, find the temperature of gas entering the superheater and the heating surface area. a. 987F, 456ft2  b. 3421F, 534ft2  c. 1445.F, 634ft2  d. 765F, 765ft2

 

a ta=?

2

flue gas U=4 BTU/hr-ft?-°F

h2=1316.4 BTU lb t2=600 °F

BTU cpg=0.241 lb-°F mg ms =1.6 lb ms=17580 hr

steam 1 h1=1202.45BTU lb t1=413 °F

b tb=1150 °F

Solution: ms(h2 – h1) = mCp(ta – t b) A = q/ U LMTD 9)

thus, ta = 1445.51 °F thus, A = 634 ft2

A 22.7kg/s 22.7kg/s flow of air air enters a preheate preheaterr at 28C and leaves leaves at 150C; 23.7kg/s 23.7kg/s of exhaust exhaust gases, gases, 2 c p=1.09kJ/kg-K, enters at 315C. The overall coefficient of heat transfer is 710 W/m -C. Determine the surface area for counterflow. a. 28.77m2  b. 22.82m2  c. 32.54m2  d. 27.49m2

  Solution:

A = q/ U LMTD where: mCpΔt ] gas= mCpΔt ] air   thus, t b = 207.15°C A = 22.82m2

10) A waste heat recovery boiler produces produces 4.8Mpa (dry saturated) saturated) steam from 104C feedwater. feedwater. The  boiler receives energy from 5kg/s of 954C dry air. After passing through the waste heat boiler, the temperature of the air has been reduced to 343C. How much steam in kg is produced per second? At 4.8mPa dry saturated, h=2796kJ/kg. a. 1.3  b. 0.91 c. 2.1 d. 3.4

Solution: ms (h b - ha) = ma Cpa (t1 – t2)

thus, ms = 1.3 kg/s

11) A steam boiler boiler generating generating 25,560 kg/hr of steam steam at 4.137Mpa and 426.7C an enthal enthalpy py of 3274.1 kJ/kg is continuously blown at the rate of 1116kg/hr with an enthalpy of 1055kJ/kg.. Feedwater  enters the economizer at 148.9C with an enthalpy of 629.87kJ/kg. the furnace burns 2700kg/hr of  coal with a higher heating value of 30,470.6kJ/kg. Calculate the overall efficiency of the steam  boiler. a. 81.78% b. 84.78% c. 82.73%  d. 79.63%

 

Solution: e bo = ( Qs/Qf ) 100%

where: Qs = mshs – m bh b – mfwhf   0

thus, e bo = 82.73% 0

C   to 12 C   in a double- pipe 0   0 C  at the rate of 0.166 kg/s. If  heat exchanger by water entering at 50 C and leaving leaving at 40 0   2 required the overall heat transfer coefficient coefficient is 850 W/m . C  , what heat exchanger area is required for counter flow ? d. 0.227m2 a. 0.527m2  b. 0.173m2  c. 0.458m2

12) In a food processing processing plant a brine solution solution is heated from 6

Solution: A = q/ U LMTD

where: q = mCpΔt

thus, A = 0.227 m2

13) A shell-and-tub shell-and-tubee heat exchanger must transfer transfer 205 kW to a solution with a specific specific heat of 3.26 0 0 kJ/kg-K kJ/kgK and change its temperatur temperaturee from 65 C  to 93 C . Steam is available at 250 kPa (tsat=127.35C). The unit convective coefficient is 3400 W/m

  2

− K   for the inside and 7300 W/m

2

-K for the outside. outside. The thermal conductivit conductivity y for the tubes is 111 W/m-K, W/m-K, and the tubes have 4.0 cm O.D. and 3.0 cm I.D. and are 3 m long. Determine the number of tubes required. required.   a.7   b.6 c.5 d.8 14) A closed feedwater heater, with a transmittance transmittance of U=350Btu/hr-ft2-F, uses condensing steam at 20  psia (tsat=227.96F) for heating 85,000lb/hr of water from 60F to 215F. What is the transmitting area? a. 627 ft2  b. 622ft2  c. 876ft2  d. 234ft2

 

Solution: A = q/ U LMTD

thus, A = 622.2 ft2

15) A deaerating heater operates at 26.7psia(tsat=242.95F) and receives water water at 181.6F. Drains from higher-pressure heaters enter in the amount of 168,000 lb/hr at 303.7F. The feedwater flow from the heater is 673,000lb/hr. Calculate the steam flow for an enthalpy of 1237.2Btu/lb. c. 191024lb/hr  d. 12,654lb/hr  a. 12102lb/hr b. 21,765lb/hr

Solution: mshs + m2h2 + m3h3 = m4h4  where: m2 = m4 – ms – m3  = 505,000ms Thus, ms = 19102 lb/hr  16) A cold storage compartment is 4.5 m long by 4 m wide by 2.5 m high. The four walls, ceil ceiling ing and floor are covered to a thickness of 150 mm with insulating material which has a coefficient of  thermal conductivity of 5.8 X 10 -2 W/ m K. Calculate the quantity of heat leaking through the insulation per hour when the outside and inside face temperatures of the material is 15°C and -5°C respectively. a. 2185kJ  b. 3652kJ c. 1254kJ d. 4658kJ

  Solution: q = AUΔt

where: U = k //x x

thus, q = 607.07 W =2185 kJ/hr.

17) The air inside electronic electronic package housing housing has a temperatur temperaturee of 50 C. A chip in this housing has internal thermal power generation rate of 0.003W. this chip is subjected to an air flow resulting in a convective coefficient h of 9 W/m-K over its two main surfaces which are 0.5cm by 1cm. determine the chip surface temperature neglecting radiation and heat transfer from edges. a. 3.33C b. 53.33C  c. 56.67C d. 23.33C

 

Solution: q = hAΔt

where: ts – 50

thus, ts = 53.33°C

18) Water enters a 3cm diameter tube with a velocity of 50m/s 50m/s and a temperature of 20C and is heated. Calculate the average unit convective coefficient. For water, kinematic viscosity= 1.006x10 -6m2/s;  prandt number=7; and thermal conductivity=0.597W/m-K. a. 86.6kW/m2-K   b. 23.45 c. 76.12 d. 123.54 19) The total total incide incident nt radian radiantt energy energy upon a body which which parti partiall ally y reflec reflects ts absorb absorbs, s, and tr trans ansmit mitss   2

radiant energy is 2200 W/m . Of th this is amount, amount, 450 450 W/   m absorbed by the body. Find the transmissivity. a. 0.486 b. 0.486 c. 0.386 Solution: Trans. = Gtrans / G

2

  is reflected and 900 W/m

where: G = Gref + Gab + Gtrans

 

  2

 is

d. 0.832

thus, Trans. = 0.386

20) What What surfac surfacee area area must must be provid provided ed by the filamen filamentt of a 100W evacuat evacuated ed light light globe globe where where t=2482C and emissivity= 0.38 for the filament? Assume the ambient temperature to be 25.6C.   a. 0.206cm2  b. 0.806 cm2  c. 1.24 cm2  d. 2.45 cm2 Solution: q = F12 ∈ A1 σ  (T14 – T24)

thus, A = 8.06 x 10-5 m2  = 0.806cm2

21) A flat circular plate is 500 mm diameter. diameter. Calculate Calculate the theoretical theoretical quantity of heat radiated radiated per  hour when its temperature is 215°C and the temperature of its surrounds is 45°C. Take the value of  the radiation constant as 5.67 X 10-11 kJ/ m2 s K 4. a. 1863kJ  b. 2658Kj c. 3652kJ d.3215kJ

4

4

Solution: q b = F12 ∈ A1 σ  (T1  – T2 )

thus, q b = 517.5 W = 1863 kJ/hr. kJ/hr.

  22) The steam drum of a waterwater- tube boiler has hemispherical hemispherical ends, the diameter diameter is 1.22 m and the overall length is 6 m. Under steaming conditions the temperature of the shell before lagging was 230°C and the temperature of the surrounds was 51°C. The temperature of the cladding after  lagging was 69°C and the surrounds 27°C. Assuming 75% of the total shell area to be lagged and taking the radiation constant as 5.67 X 10 -11kW/ m2 -K 4, estimate the saving in heat energy per hour  due to lagging. c. 166915kJ  a. 157000kJ b. 187500kJ d. 96852kJ

 

Solution: Savings in Heat = Net area after logging (R  bef  bef - R aft aft) 4 4 thus, Savings = 46365.4 W = 166915 kJ/hr  where: R: E/A = σ  (T1  – T2 ); 23) Determine Determine the monochromatic monochromatic emissive emissive power at 1.30 1500

  0

a. 1233 

μ m of a blackbody blackbody at a temperat temperature ure of 

F.

Btu   hr − ft 2− μm

b. 42 038

Btu Btu Btu   c. 41,365   d. 32564 2 2 hr − ft  − μm hr − ft  − μm hr − ft 2− μm

24) Saturated Saturated steam at 500K flows in a 20cm-ID, 20cm-ID, 21cm-OD, pipe. The pipe is covered with 8cm of  insulation that has a thermal conductivity of 0.1W/m-K. The pipe’s conductivity is 52W/m-K. The ambient temperature is 300K. The unit convective coefficient on the inside is 18,000W/m 2-K and on the outside is 12W/m 2-K. Determine the heat loss from 4m of pipe. a. 721W

b. 1023W

c. 987W

Solution: q = AUΔt

d. 821W

thus, q = 821.96 W

25) An insulated steam pipe passes through a room in which the air and walls are at 250 C. The outside diameter of the pipe is 70mm, and its surface temperature and emissivity are 200 0  C and 0.8 respectively. If the coefficient associated with free convection heat transfer from the surface to the air is 15W/m2-K, what is the rate of heat transfer loss from the surface per unit length of pipe? a. 698W/m b. 1243W/m c. 998W/m  d. 876W/m Solution: qT = qconvection + qradiation where: qconvection = hAΔt ; qradiation = F ∈ A σ  (T14 – T24) Thus, q/L = 997.85 W/m 26) The hot combustion combustion gases of a furnace furnace are separated separated from the ambient ambient air and its surrounding, surrounding, 0 which are at 25  C, by a brick wall 0.15m thick. The brick has a thermal conductivity of 1.2W/m-K  and 0a surface emissivity of 0.8. Under steady state conditions and outer surface temperature of  100  C is measured. Free convection heat transfer to the air adjoining this surface is characterized  by a convection coefficient of 20W/m2-K. What is the brick inner surface temperature in C? a. 352.5  b. 623.7 c. 461.4 d. 256.3

Solution: q = k A(t A(t1 – t2) /  x  =hAΔt + F ∈ A σ  (T14 – T24)

thus, t1 = 352.5°C

 

27) A cubical tank of 2 m sides is constructed of metal plate 12 mm thick contains wat water er at 75°C. The surrounding air temperature is 16°C. Calculate the heat loss through each side of tank per mi minute. nute. Take the coefficient of thermal conductivity of the metal as 48 W/mK, the coefficient of heat transfer of the water 2.5 kW/m²K, and the coefficient of heat transfer of the air 16 W/m²K. a. 229.3kJ b. 214.3kJ c. 124.3kJ d. 224.3kJ

1

Solution: q = AUΔt

where: U =

( )( )  1

hi

+

 x  1 +( )   k  ho

thus, q = 224.2 kJ/min.

k =45.0 W / m⋅ K )  having a 5.0 cm OD is covered with a 4.2 cm thick layer of  whic ich h is in turn turn co cover vered ed wi with th a 3.4 3.4 cm la layer yer of fi fibe berg rgla lass ss magnes mag nesia ia (   k =0.07 W / m⋅ K ) wh

28) A steel steel pipe pipe (

insulation( k=0.048 W/m-K). The pipe wall outside temperature is 370 K and the outside surface temperature of the fiberglass is 305 K. What is the interfacial temperature between the magnesia and the fiberglass? a. 329.6 K   b. 329.1 K c. 329.9 K d. 329.25 K 

Solution: q b-c = qc-d 

where: q =

 Δt 

¿¿

 

thus, tc = 329.6 K 

29) Determine the critical radius in cm for an asbestos-cement covered pipe. 2

k asb =0.208 W/m   ¿ K 

0

.The external heat-transfer coefficient is 1.5 Btu/h   ¿ ft  ⋅  F . a. 2.24 cm b. 2.55 cm c. 2.66 cm d. 2.44 cm  /n Solution: r c = k /n

thus, r c = 0.0244 m =2.44 cm

  30) A 6 in thick concrete concrete wall, having thermal conductivity conductivity air at 70

  0

F on one side and air at 20

  0

k  =0.50 Btu/h

0

  ¿ ft ⋅ F  , is exposed to

F on the opposite side. The heat transfer coefficients are

 

hi =2.0 Btu/h   ¿ ft 2⋅0 F  on the 70  F  side and   0

h0

2

=10 Btu/h   ¿ ft 

¿0 F  on the 20   0 F 

side. Determine the heat transfer rate.   a. 31.25 BTU/hr-ft2  b. 33.52 BTU/hr-ft2  c. 56.6 BTU/hr-ft2  d. 76.8 BTU/hr-ft2

thus, U = 0.625 BTU/hr.ft2.°F

Solution: q = AUΔt

31) A hollow steel sphere contains a 100-watt 100-watt electrical electrical filament, filament, and these data are known; r    i =9 hi =6 ,   ho = 2 Btu hrin., r   0 =12 in. The film coefficient for the inner and outer surfaces are   0   2   0 F. Assuming the steady state, compute the ft -  F  ; the environmental temperature is 80 temperature inside air  0 0 0 0 c. 101.9  F  d. 101.5  F   b. 110.8  F      a.102.9  F 

1

Solution: q = AUΔt

where: U =

( )+(   1

hiAi

)

  ro− ri   1 +( )  hoAo 4 πrorik 

thus, ti = 101.96°F

32) If a triangle of height d andtobase b istervertical and submerged in a liquid with it itss vertex at the liquid surface, compute the depth its center cen of pressure.   a. ¾ d  b. 2/3 d c. 2/5 d d. ½ d

3/4d

Solution: hcp = 2/3d + e

where: e = I/AYcg ; I = bh 3/ 36   ; Ycg =  h cg  = 2/3d

thus, h cp =

 

33) Gate AB is vertical and 5 ft wide by 3ft high hinged at point A and restrained by a stop at point B. If  stop B will break if the force on it reached 9000lb, find the critical water depth.   a. 24.23ft b. 22.3ft c. 20.23ft  d. 24.32ft

Solution: FH (1.5 + e) = 900 (3) where: e = I/AYcg ; Ycg = hc – 1.5; FH = γA hg thus, hc = 20.23 ft. 34) The weight of a certain crown in air was found to be 15N and its weight in water is 12N. Compute Compute its specific gravity. b. 5    a. 10.77 c. 10.86 d. 11.25 Solution: Sp = N/F B = 5  35) A balloon balloon weighs 300 lb and has a volume volume of 15,000ft 15,000ft3. It is filled with helium, which weighs 0.0112pcf at the temperature and pressure of the air, which weighs 0.0807 pcf. What load will the  balloon support? c. 742.5.8lb  d. 812.4 lb   a. 765.5lb b. 870.2 Solution: WHe + W bal + Wload = FB 

where: WHe = γHe V bal

thus, Wload = 742.5 lb

36) If the center of gravity of a ship in the upright upright position position is 10m above the center of gravity gravity of the  portion under water, the displacement being 1000metric tons, and the ship is tipped 30 0 causing the center of buoyancy to shift sidewise 8m. What is the value of the moment in kg-m?   a. 3M kg-m  b. 3.5M kg-m c. 4M kg-m d. 2M kg-m Solution: M= Wx Wx = F bx; W=1000,000kg ; x = MG sin 300; MG= MBO-GBO; GBo= 10m   MBo=8/sin30o=16m; then MG = 16-10 = 6m, 6 m, thus x = 6sin 30 0= 3m   M = 1,000,000kg(3m) = 3,000,000kg-m = 3M kg –m 37) An open tank 1.82m square, weighs 3,425N and contai contains ns 0.91m of water. It is acted upon by an unbalanced force of 10,400N parallel to the pair of sides. What must be the height in m of the sides of the tank so that no water will be spilled? d. 1.2   a. 1.5 b. 1.3 c. 1.4 Solution: h – height of tank    h = 0.91m + x; x = 0.91(a/g); REF = W(a/g) = 10400N; W = 3425 + 9806.6(0.910)(1.82) 2= 32, 984.9; a/g = 0.3153; x = 0.91 + 0.91(0.3153) = 1.2m 38) An open vessel 30cm in diameter and 90cm high is filled with water to a depth of 45cm. Find the magnitude of the velocity in rad/s such that the vortex is just at the bottom.

 

  a. 21.01

b. 28.01 

c. 12.22

c. 34.2

Solution: y = w2x2/(2g)

where y=0.9m x = 0.15m and solving for w = 28.01rad/s

39) A liquid of specific gravity 1.75 flows in a 6cm horizontal pipe. The total energy at a certain point in the flow is 80m. The elevation of the pipe above a fixed datum is 2.6m. If the pressure at the specified point is 75kpa, determine the velocity of flow and the power available at that point.   a. 37.85m/s; 146,979 W  b. 44.29, 84372 c. 35.43, 98262 d. 33.38, 78933 Solution: Ht = z + v2/2g + p/γ Ht = 80m, z= 2.6m p =75 sg =1.75 γ = 1.75(9.81) =17.17   Solving for v2/2g = 70.031 and v =37.85m/s finally P = γQH = 146979W 40) If the velocity of water is 8m/s and the pressure is 140kPa on the discharge side of a pump. is the head of the pump if the velocity is 4m/s and pressure is 90kpa before the pump? a. 6.54m b. 7.98m c. 7.54m  d. 6.82m

What

Solution: H = (140 – 90)/9.81 + (82 – 42)/(2(9.81)) = 7.54m 41) A 300mmx7 300mmx75mm 5mm venture venture meter meter is inserted inserted in a 300mm 300mm diamet diameter er pipeli pipeline ne where where water water flows flows at 55L/s. Neglecting losses, compute the drop in pressure head from the inlet to the throat. d. 7.9m a. 5.9m b. 4.3m c. 6.4m Solution: ( p1- p2)/γ = (v22 – v12)/2g v1 = Q/A1= 0.778m/s v2=Q/A2= 12.45m/s   Thus ( p1- p2)/γ = 7.87m 42) The headloss in 50m of 12cm diameter pipe is known to be 6m when li liquid quid of specific gravity of 0.9 3 and viscosity of 0.04pa-s at the rate 0.06m /s.Find the shear stress at the wall of the pipe. d. 63.56 kpa a. 31.6kpa b. 15.8 kpa c. 126.4pkpa Solution: Ss = ghf Dρ/4L Dρ/4L = 63.56Pa 43) Water flows flows at 0.2m3/s through a 300mm diameter, 120m long pipe under a pressure difference of  280mm Hg. Compute the friction factor. a. 0.023  b. 0.0435 c. 0.0154 d. 0.0876 Solution: f = 2ghf D/Lv D/Lv2  Solving for f = 0.023.

hf  =   = 280(13.6) = 3.808mWater v = Q/A = 2.829m/s

44) A square concrete concrete conduit having having a side of 0.788m carries carries water at a rate of 4m 3/s. Using Hazen William formula with C=120, compute the head loss if the length of the conduit is 45m. a. 2.8m b. 1.8m  c. 1.3m d. 2.1m Solution: v = 0.8492 ChwR hS0.54m/s  

R h = A/wetted perimeter = 0.197m solving for S = 0.04001

But S = hf /L thus hf  = 1.8m.

45) Find the equivalent length of 167mm diameter diameter pipe, f=0.024 for a reentr reentrant ant pipe entrance with k=1.   a. 6.958m  b. 7.394m c. 6.807m d. 7.102m Solution: Le = K mD/f = 6.958m 46) Two pipes with the same same frict friction ion factor factor and length length are parallel parallel.. If the fir first st pipe has twice twice the diameter of the second, what must be the ratio of their flow   a. 4.66 b. 4.32 c. 5.66  d. 10.22 Solution: For parallel pipes:   Headloss are equal: hf1 = hf2 = fLDv2/2gD   Flow: Q1 + Q2 = QT   But: L1 = L2; f 1 = f 2 Thus v21/D1 = v22/D2 or v12/v22 = D1/D2 = 2 or v1/v2 =   Also: Q2 = A2v2  and Q1= A1v1  then Q1/Q2 = 4v1/v2 = 4 2  = 5.657.

2

47) with A 16cm diameter pipe length 200m and surface elevati elevation on of 50m the discharge dischar ge of pipe f=0.03 and loss of of head due to entrance coefficient k=0.5 what is from the velocity of flow in the m/s?   a. 5.09m/s b. 6.05m/s c. 4.95m/s  d. 3.56m/s

 

2 Solution: z1 = v22/2g + hL  Where hL= hentrance + h pipe + hexit = K ev2/2g + fLv2/2gD + K exit exitv /2g   hL = (0.5 + (0.03(200))/0.16 + 1) v2/2g = 39v2/2g   finally 50m = v2/2g + 39v2/2g and solving for velocity v = 4.95m/s. 

48) Horizo Horizonta ntall orific orificee under under a consta constant nt head of 1.3m is issue suess a jet which which hits hits a point point 5m below below the centerline of the orifice and 5m horizontally from the vena contracta. What is the coefficient of  velocity? a. 0.98  b. 0.95 c. 0.9 d. 0.89   Solution: Cv = vactual/videal  where vactual = -gx2/2y x = 5m y = -5m vactual = 4.95m/s   videal =√ 2 gh = 2 ( 9.81 ) ( 1.3)= 5.05m/s thus Cv = 4.95/5.05 = 0.98.

49) What What is the dischar discharge ge capacity capacity if a concre concrete te pipe culver culvertt 4ft in diamet diameter er and 10m long if the difference in water level at the outlet is 1.52m. 1.5 2m. Assume coefficient of discharge of 0.74.   Solution: Vel = √  2 gΔh   Qactual =Cd Vel A ; thus, Qactual = 4.72 cu. m/ s 50) A 35,000 kW plant has a util utilizati ization on factor of 71 % and a load factor of 39.6 %. What is the average load in the plant? b. 9840.6kW  c. 10254.3kW   a. 7654.2kW d. 12365.2kW  

Solution: AL = (LF) (UF) (PC)  

where: PC = 35000 kW; UF = 71%; LF = 39.6%

Thus, AL = 9840.6 kW

51) The annual peak load on a 15,000kW power plant is 10,500kW. Two substations substations are supplied by this  plant. Annual energy dispatched through substation A is 27,500,000 kW-hr with a peak at 8900kW, while 16, 500,000 are sent through B with a peak 6650kW. Neglect line losses. Find the diversity factor between substations and the capacity factor of the plant.   a. 2.32; 53.6% b. 1.23; 65.3% c. 1.48; 33.48% d. 1.35; 75.46%  

Solution:

GDF =

∑  MDsubstations    MDplant 

where: MDsub= 8900 + 66500 (kW); MD plant = 10500 (kW)

Thus, GDF = 1.48  

CF =

 AL    PC 

where: AL =

 E 8760

; E= EA + EB thus, CF = 33.48%

52) A furnace burns coal with the ff. ultimate analysis:

C=80.17%, H=4.34%, O=2.69%, N=1.45%,

S=0.84%,, A=7.09% W=3.42% S=0.84% W=3.42% For 15% excess air and complete complete combustion. combustion. Determine Determine the actual air needed per kg if water is to be included and air is is at 28C and 0%RH(w=0.0143kgv/kgda). a. 10.32 b. 9.78 c. 12.43  d. 15.43 Solution: A/F” = A/F (1+e) (1+w)  

[  ]

 H − where: A/F = 11.53C + 34.36  H 

O

 + 4.32S

8

thus, A/F” = 12.43

  53) A natural gas has the following percentage volumetric composi composition. tion.   CH4=59.8%, C2H6=37.6%,  N2=2.2%, CO2=0.4%. Calculate for complete, the the weight of air air supplied including moisture moisture if air  is in excess of 25% and at 28C and 50% RH(0.012kgv/kgda).   a. 12.45 b. 20.27  c. 23.35 d. 11.23 Solution: A/F” = A/F (1+e) (1+w)  

[  ]

 H − where: A/F = 11.53C + 34.36  H 

H=0.21479; N2 = 0.02846; CO2 = 0.00296

thus, A/F” = 20.27

O 8

 + 4.32S; C = 0.75083;

 

54) Two hundred hundred metric metric tons per hour of coal coal are burned burned in 125% 125% stoich stoichiom iometr etric ic air air;; the as fi fired red ultimate analysis is 75%C, 4%H, 0.5%S, 6%O, 1.5%N, 8%W, 5% Ash. Find the mass of air needed to burn the fuel. a. 2446.45mton/hr  b. 3652.3mton/hr c. 4526.2mton/hr d. 6532.2mton/hr 

[  ]

 H − Solution: mair = (mfuel) (A/F’) where: A/F’= A/F (1+e); e=25%; A/F = 11.53C + 34.36  H   

4.32S; mfuel = 200mton/hr

O 8

 +

thus, mair  =  = 2446.45 mton/hr 

55) C8H18  fuel is burned with with 25% excess. Calculate the weight weight of air needed including mois moisture ture if air  is at 25C and 60% RH.(w=0.012). b. 19.04  a. 12.30 c. 20.23 d. 21.35   Solution: A/F” = A/F (1+e) (1+w) 56)

where: A/F = 15.05 (balancing)

thus, A/F” = 19.04

A vertical vertical jet of water water supports supports a load of 200N at a constant vertical height height of 2m from the tip of the nozzle. The diameter of the jet is 25mm. F Find ind the velocity of the jet at the nozzle tip. a. 23.28m/s b. 28.32m/s c. 21.13m/s  d. 22.82m/s  

Solution: Vi ² =V    + 2   h  where: F jet =  ρV Vel2 = 200N; Vel2 = 20.105 m/s Thus, Vf 2 = 21.13 m/s

57) A 50mm horizontal jet of water with a discharge of 0.054m3/s strikes a vertical wall at 90 0 to the wall. What is the force exerted on the wall? a. 1.49kN  b. 2.19kN c. 1.39kN d. 1.19kN   Solution: Fw = F j = ρQVel where: Vel = Q / A  = 27.50 m/s

58)

thus, Fw =1485 N =1.49 kW

A cylindrical tank (10m in diameter and 5m in depth) contains water at 20C (9.789kN/m3) and is brimful. If the water is heated to 50C (9.689kN/m3), how much water will spill over the edge of the tank? a. 4.05m3  b. 4.1m3  c. 5.1m3  d. 3.67m3 Solution: Vspill = Vtank ( γ20 – γ50) / γ50 where: Vtank  =  = π/4 (D 2) H; γ20 =9.789kN/m3; 3 thus, Vspill = 4.05 m γ50=9.689kN/m

59) Two large plane surfaces are 1 in apart, and the space between them is filled with with a liquid of 2 absolute viscosity 0.02000 lb-sec/ft . Assuming the velocity gradient to be a straight line, what force is required to pull a very thin plate of 4 ft2 area at a constant speed of 1 ft/sec if the plate is 1/3 in from one of the surfaces? a.) 7.82lb. b.) 5.67lb c.) 56.7lb d.) 4.32lb  

Solution: F = Ff1 + Ff2

where: Ff = (μAVel)/y

thus, F =4.32 lbs.

60) A cylinder of 0.122-m radius rotates rotates concentrically insi inside de a fixed cylinder of 0.128-m radius. Both cylinders are 0.305 m long. Determine the viscosity of the liquid that fills the space  between the cylinders if a torque of 0.881N-m is required to maintain an angular velocity of 60revolutions per minute.   a. 0.34 Pa-s b. 0.65pa-s c. 0.24pa-s  d. 0.87pa-s  

Soluti Solution: on: T = F f   R wher where: e: Ff = (μAVel)/Cr ; Ve Vell = 2π 2πRN RN;; A= A= 2π 2πRL RL T=(4π R  LNμ)/Cr therefore μ=0.24 Pa.s 2

th thus us,,

3

61) A small drop drop of water at 80 0F is in contact with the air and has diameter 0.02 in. If the p pressure ressure within the droplet is 0.082 psi greater than the atmosphere, what is the value o off the surface tension?  

a. 0.00492 lb/ft 

b. 0.00654lb/ft

c. 0.00876lb/ft

d. 0.00043lb/ft

 

 

Solution: o =

 D ( ΔP ) 4

  =0.00041 lb/in. =0.00492 lb/ft.

1. Determine Determine the the ASHRAE number number designati designation on for dichlorot dichlorotetrafl etraflouroet ouroethane, hane, CClF2CClF2. a. 114  b.123 c. 124 d. 125 Reference: Heating, Ventilating, and Airconditioning: Analysis and Design by Macqueston, Parker and Spitler page 542. 2. Which of the the following following refrigera refrigerant nt does not belong belong to A1 Safety group group classific classification ation?? a. R11 b. R13 c. R114 d. R21 Reference: Heating, Ventilating, and Airconditioning: Analysis and Design by Macqueston, Parker and Spitler page 539. 3. A stra strain iner er has has a coef coeffi fici cien entt Cv rating of 60. It is to be used in a system to filter 50gpm of water. What pressure loss expressed in feet of water can be expected? a. 1.6  b. 2.31 c. 3.25 d. 0.85 2 Solution: hf  =  = 2.31(Q/Cv) = 1.6ft of water  4. Comput Computee the volume of expansio expansion n tank for a chill chilled ed water system system that that contains contains 2000gal 2000gal of  water. The system is regulated to 10psig at the tank with an operating temperature of 45F. It is estimated that the maximum water temperature during extended shutdown would be 100F and a safety relief valve in the system is set for 35psig. Assume standard barometric pressure and steel  pipe. Take specific volume at 100F as 0.01613ft3/lb and at 45F as 0.01602ft3/lb. d. 5.2ft3 a. 3.2ft3  b. 8.6ft3  c. 10.2ft3  Solution: The volume of expansion tank is given by the formula:

V w  

V T =

v2 −1 −3 α ∆ t  v1

[( −)

 P a  Pa  P 1  P2

]

  Substituting values with P 1=24.696psia, P2=49.696psia, v1=0.01602, v2=0.01613, α=6.5x10-6, t1=45F, t2=100F and solving we get VT=5.2ft3. 5. Estima Estimate te the exit temper temperatu ature re of 1000cfm 1000cfm of air at 120F flowing flowing in a 16in 16in round duct duct 24ft in length. The duct has 1in of fibrous glass insulation, and the overall heat transfer coefficient  based on outside surface is 0.2Btu/(hr-ft 0.2 Btu/(hr-ft2-F). The environment temperature is 12F. Take average density of air as 0.067ft3/lb. a. 108F b. 117F  c. 125F d. 136F Solution: q = AUΔti-o = mc pΔtin-exit = QρCPΔtin-exit  A = πdoL   substituting values and solving for texit; texit=117F 6.