Turbomachine Example Question

EG 362 – Fluid Mechanics TURBOMACHINES TURBOMACHIN ES EXAMPLES

1.

The The buck bucket etss of a Pel Pelto ton n whee wheell rota rotati ting ng at at 65 r.p r.p.m .m.. are are situ situat ated ed at at a radi radius us of 0.75 m from the axis of rotation and the water jet issues from the nozzle with a speed of 12 m/s. The volume flow rate is 0.5 m 3/s and the buckets deflect the flow through 160 0 while slowing slowing down the speed of the water, relative to the bucket surface, by 15%. Calculate: i) ii) iii) iv) iv) v)

the diameter of the jet; the for force of the jet jet on the bucket; et; the power output; the the eff effic icien iency cy at this this speed speed,, assu assumi ming ng no mech mechan anica icall los losses ses;; the maximu imum hydrau raulic eff efficiency ency and and the rotational spe speed at which it occurs.

[ i) 230 mm; ii) 6.2 kN; iii) 31.7 kW; iv) 88%; v) 90%, 76.4 rev/min ] 2

Waterr und Wate under er a head head of 270 270 m is is avai availa labl blee for for a hy hydrodro-el elec ectr tric ic pow power er sta stati tion on and is to be supplied through three pipes 2.4 km long in which the friction loss is 24 m. The inlet and fittings losses are negligible. It is decided to install a number of single jet Pelton wheels with a specific speed N, not exceeding 38 (rev/min, kW and m units), to produce a total output power  of 18,000 kW. The wheel speed is to be 650 rev/min and the ratio of   bucket speed to jet speed 0.46 Assume that the overall efficiency is 87% and that the coefficients of  discharge and velocity of the nozzles is 0.94 and 0.97 and estimate: i) ii) iii) iv) iv)

the nu number of of Pe Pelton wh wheels re required the wheel diameter   the jet diameter   the the diam diamete eterr of of the the supp supple le pip pipes es if if the the fric fricti tion on facto factorr is .006 .006

[ i) 6; ii) 907 mm; iii) 167 mm; iv) 1.102 m ] 3

An inwa inward rd-f -flo low w reac reacti tio on turb turbin inee has has an inl inlet et gu guide ide van vane angl anglee of 30 300 and the inlet edges of the runner blades are at 120 0 to the direction of whirl. The breadth of the runner at inlet is a quarter of the diameter at inlet and there is no velocity of whirl at outlet. The overall head is 15 m and the speed 16.67 rev/s. The hydraulic and overall efficiencies may be assumed to be 88% and 85% respectively. Calculate the runner diameter at inlet and the power developed (The thickness of the blades may be neglected) [ 251 mm; 35.2 kW ]

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A ver verti tica call shaf shaftt inwa inward rd flow flow reac reacti tion on turb turbin inee runn runner er dev devel elop opss 12, 12,50 500 0 kW kW 3 and uses 12.3 m /s of water when the net head is 115 m. The runner has a diameter of 1.5 m and rotates at 430 rev/min. Water enters the runner 

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EG 362 – Fluid Mechanics without shock with a radial velocity component of 9.6 m/s and passes from the runner to the draft tube without whirl with a velocity of 7.3 m/s. The difference between the sum of the pressure and potential heads at the entrance to the runner and at the entrance to the draft tube is 60 m. The mechanical efficiency may be assumed to be 100%. Determine: i) ii) iii) iv)

the efficiency the velocity and direction of the water entering the runner from the fixed guide blades the entry angle of the runner blades the loss of head in the runner 

[ i) 90%; ii) 31.5 m/s, 17 0 42’; iii) 1110 6’; iv) 4.2m ] 5

A vertical shaft Francis turbine has an overall efficiency of 90% and runs at 7.14 rev/s with a water discharge of 15.5 m 3/s. The velocity at the inlet of the spiral casting is 8.5 m/s and the pressure head at this point is 240 m, the centre-line of the casting inlet being 3 m above the tail-water level. The diameter of the runner at inlet is 2.23 m and the width at inlet is 300 mm. The hydraulic efficiency is 93%. Determine: i) ii) iii) iv) v)

the output power   the ‘dimensionless specific speed’ the guide vane angle the runner blade angle at inlet the percentage of the net head which is kinetic at entry to the runner 

Assume that there is no whirl at outlet from the runner and neglect the thickness of the blades. [ i) 33.8 MW; ii) .0773 (rev); iii) 9.31 0; iv) 124.20; v) 43% ] 6

An axial flow turbine, with fixed stator blades upstream of the rotor, running at 250 rev/min has an outer diameter of 1.8 m and an inner  diameter of 0.75 m. At the mean diameter the outlet angle α  of the stator   blades is 40% and the inlet angle β  of the rotor blades is 150 0, both measured from the direction of the blade velocity. Determine: i) ii) iii)

the flow rate for which the angle of the incidence for the rotor   blades is zero assuming that the axial velocity is uniform the rotor blade angle at outlet if the whirl component there is zero the theoretical power output if the change of whirl is independent of the radius.

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EG 362 – Fluid Mechanics

[ 12 m3/s; 18.90; 1.36 MW ] 7

If the no-flow head rise from a centrifugal pump is H metres, the rotational speed N rev/min and the external diameter of the impeller D metres, show that  N 

84.6

H 

=

 D

Assume that the pressure rise is due solely to the forced vortex swept out  by the impeller. A centrifugal pump delivers 1.27 m 3 of water per minute at 1200 rev/min. The impeller diameter is 350 mm and the breadth at outlet 12.7 mm. The  pressure difference between the inlet and outlet flanges is 272 kN/m2. If  the manometric efficiency is 63%, calculate the impeller exit blade angle. [ 32.80 ] 8

A centrifugal blower has an impeller of outer diameter 500 mm and width 75 mm with vanes set back at 70 0 to the tangent at the outer periphery. When the blower is delivering air weighing 1.25kg/m 3 at a rate of 3.1 m3/s, the speed is 900 rev/min and the pressure difference across the blower  measured by a manometer is 33 mm of water. The power supplied to the  blower shaft is 1.65 kW and the mechanical efficiency is 93%. Assuming radial inlet to the impeller and neglecting the thickness of the vanes, find the manometric and the overall efficiencies. Also determine the power lost in i) ii) iii)

bearing friction the diffuser   the impeller and inlet

[ 78.6%, 60.8%; i) 116 W; ii) 272 W; iii) 258 W ] 9

A centrifugal pump running at 700 rev/min is supplying 9 m 3/min against a head of 19.8 m. The blade angle at exit is 135 0 from the direction of  motion of the blade tip. Assume that the relative velocity of the water at exit is along the blade and that the absolute velocity at inlet is radial. The radial velocity component of flow is constant at 1.8 m/s. Calculate the necessary impeller diameter  i) ii)

if none of the energy corresponding to the velocity at the exit from the impeller is recovered if all of this energy is recovered

In case i) find also the width of impeller at exit, allowing 8% for vane thickness.

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EG 362 – Fluid Mechanics [ 542 mm; 406 mm; 53 mm ] 10

A centrifugal pump, having four stages in parallel, delivers 11 m 3/min of  liquid against a head of 24.7 m, the diameter of the impeller being 225 mm and the speed 1700 rev/min. A pump is to be made up with a number of identical stages in series, of  similar construction to those in the first pump, to run at 1250 rev/min and to deliver 14.5 m 3/min against a head of 248 m. Find the diameter of the impellers and the number of stages required. [ 433 mm, 5 ]

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A centrifugal pump running at 1000 rev/min has the following characteristics: Discharge (m3/min) Head (m)

0 22.5

4.5 22.2

9.0 21.6

13.5 19.5

18.0 14.1

22.5 0

The pump is connected to a 300 mm diameter suction and delivery pipe of  total length 69 m which discharges to atmosphere at a height of 15 m above the reservoir level. The inlet loss is equivalent to an additional 6 m length of pipe and the friction factor is .006. Find the rate of flow. Explain how you would find the rotational speed to which the pump must  be decreased in order to reduce the flow to one half of this rate. [ 14 m3/min; 855 rev/min ]

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