Problems 244 294

Problem 244 A liquid of specific gravity 1.75 flows in a 6 cm horizontal pipe. The total energy at a certain point in the flow is 80 J/N (Joules per Newton). The elevation of the pipe above a fixed datum is 2.6 m. If the pressure at the specific point is 75 kPa. 1. Determine the velocity of the flow. 2. Determine the discharge. 3. Determine the power available at the specified point in watts. Problem 245 The pipe flow in the figure is driven by pressurized air in the tank. Assuming f = 0.014 and the flow rate is 16.60 liters/sec. 1. Find the velocity in the pipe. 2. Find the head loss in the pipe neglecting minor losses. 3. Find the gauge pressure needed to provide a flow rate of 13.60 liters/sec in kPa. Problem 246 If the velocity of water is 8 m/s and the pressure is 140 kPa on the discharge side of a pump. 1. What is the head of the pump if the velocity is 4 m/s and the pressure is 90 kPa on the side of the pump? 2. How much power is required to drive it if the diameter of the suction side is 600 mm. 3. If the pump is rated at 120 hp, what is the efficiency of the pump neglecting energy losses in the system? Problem 247 The pump in the figure discharges water at 30 liters/sec. Neglecting losses 3 and elevation changes. Assume unit weight of water is 9.79 kN/ m . 1. Determine the energy added to the water by the pump. 2. Determine the power delivered to the water by the pump. 3. Determine the mechanical efficiency of the pump if the power input recorded is 27.34 hp. Problem 248

In the syringe as shown in the figure, the drug has a mass density of 900 3 kg/ m and an absolute viscosity μ = 0.002 Pa-s. Neglecting head loss in the larger cylinder. 1. Which of the following gives the value of the Reynolds number for a flow of 0.4 mL/sec through the needle. 2. Which of the following gives the head loss. 3. Which of the following gives the force required to produce a flow of 0.4 mL/sec. Problem 249 Water is discharged through a nozzle having a diameter of jet of 100 mm at a velocity of 60 m/s at a point 240 m. below the reservoir. 1. Compute the total head loss. 2. Compute the horsepower produced by the jet. 3. Compute the power lost in friction. Problem 250 Water flows through a pipe at 5 liters/sec, if gauge pressures of 12.5 kPa, 11.5 kPa, and 10.3 kPa are measured as P1 , P2 and P3 respectively, c0mpute the following: 1. Head loss between 1 and 2. 2. Head loss between 1 and 3. 3. Head loss between 2 and 3. Problem 251 3 A 60 mm diameter pipe as shown contains glycerin ( ρ = 1258kg/ m )at 3 8.5 m /hr .

1. Compute the velocity of glycerine flowing inside the pipe. 2. Compute the Reynold’s number if μ = 1.49 Pa-s/ 3. Compute the head loss of these pressures. Problem 252

A 50 mm diameter siphon is drawing oil (sp.gr. = 0.82) from oil reservoir as shown on the figure. The head loss from point 1 to point 2 is 1.50 m and 3 from point 2 to 3 is 2.40 m. Unit weight of water is 9.79 kg/ m . 1. If the total length of the 50 mm diameter siphon is 8 m, compute the friction factor f. 2. Compute the discharge of oil from the siphon. 3. Compute the lowest vacuum pressure of the siphon. Problem 253 In the friction free siphon shown, compute the following. 1. Pressure of the water in the tube at B. 2. Pressure of the water in the tube at A. 3. If the vapor pressure of water is 0.1799 m of water, how high “h” above the free surface can point B before the siphon action breaks down. Assume atmospheric pressure is 101 kPa. Problem 254 The siphon in the figure shown is filled with water and discharging at 150 liters/sec. Compute the following. 1. Value of K used for the total head loss

kv 2 2g .

2. Losses from point 1 to point 3 in terms of velocity head

v2 2g .

3. Pressure at point 2 if two thirds of the losses occur between point 1 and 2. Problem 255 Water enters a pump through a 250 mm diameter pipe at 35 kPa. It leaves the pump at 140 kPa through a 150 mm. diameter pipe. If the flow rate is 150 liters/sec. 1. Compute the velocity of discharge pipe. 2. Compute the energy added by the pump. 3. Find the horsepower delivered to the water by the pump. Assume suction and discharge sides of pump are at the same elevation. Problem 256

In the fountain shown in the figure, water flows steadily up the vertical pipe, enters the annular region between the circular plated and emerges as a free sheet. The pressure at A is 70 kPa gage. Neglecting friction. Assume 3 unit wt. of water is 9.79 kN/ m . 1. Compute the velocity of water at A. 2. Compute the velocity of water at E. 3. Compute the volume of flow of water. Problem 257 Water flows radially outward in all direction from between two horizontal circular plates which are 120 cm. in diameter and placed parallel 25 cm. apart. A supply of 28 liters/sec being maintained by a pipe entering one of the plates at its center, 1. What is the velocity at point A? 2. What is the velocity at point B? 3. What is the pressure at point A, 15 cm from the center if no loss of friction be considered? Problem 258 The upper circular plate is horizontal and is fixed in position while the annular plate is free to move vertically and is not supported by the pipe in the center. Water is admitted at the center at the rate of 56 liters/sec. and discharges into the air around the periphery. The annular plate weighs 22 N and the weight of water on it should be considered. If the distance between the two plates is maintained at 2.5 cm. 1. Find the velocity of water around the periphery. 2. Find the pressure at point A, 150 mm from the center of the pipe. 3. What is the total weight “w” that it can support? Problem 259 Oil with a sp.gr. of 0.86 is being pumped from a reservoir shown. The pressures at points 1 and 2 are -4 psi and 43 psi respectively. The rate of 3 flow in the pipe is 0.50 ft /sec. The pump is rated at 8 hp, compute the following: 1. The head added by the pump. 2. The output hp of the pump.

3. The efficiency of the pump. Problem 260 An 8 hp pump is installed near the reservoir container oil having a sp.gr. of 3 0.82. the rate of flow of the pipe is 0.014 m /s. The pressure heads at 1 and 2 are -28 kPa and +290 kPa respectively. 1. Compute the head added by the pump. 2. Compute the output hp of the pump. 3. Compute the efficiency of the pump. Problem 261 The water tank in the figure is being filled through section 1 at v 1 = 5 m/s 3 and through section 3 at Q3 = 0.012 m /s. If the water level “h” is constant.

1. Compute the discharge at 2. 2. Compute the exit velocity at 2.

dh 3. If the water level varies and v 2 = 8 m find the rate of change dt

when d = 1.0 m. Problem 262 A 60 mm diameter siphon is drawing water from an oil reservoir as shown. If the head loss from 1 to 2 is 1.40 m and from 2 to 3 is 2.30 m. 1. Find the velocity of flow at 3. 2. Find the discharge of oil from the siphon. 3. Find the oil pressure at 2. Problem 263 3 The horizontal wye fitting in the figure splits Q1 = 4 ft /s and P1 = 20 psig. Neglecting losses, compute the following.

1. Velocity at 2. 2. Pressure at 2. 3. Pressure at 3. Problem 264

In the water flow over the spillway, the velocity is uniform at sections 1 and 2 and the pressure approximately hydrostatic. Assuming a unit width and neglecting losses, compute the following: 1. Velocity at 1. 2. Velocity at 2. 3. Rate of flow. Problem 265 Water is being pump from reservoir A to reservoir B as shown. The total length of pipe is 1090 m, and a diameter of 600 mm. The rate of flow in the 3 system is 0.65 m /s. 1. Compute the head loss in the pipe system if c = 120. 2. Compute the head added by the pump. 3. Compute the horsepower required to drive if the pump is 72% efficient. Problem 266 Oil with sp.gr. of 0.87 is being pump from a lower reservoir to an elevated tank as shown. The pump in the system is 78% efficient and is rated 185 kW. 1. Determine the flow rate of the oil in the pipe if the total head loss from point 1 to point 2 is 12 m of oil. 2. Determine the energy added by the pump. 3. Determine the velocity of flow of 160 mm diameter pipe. Problem 267 For the pump shown, the total friction head loss is 6m. If the pump delivers 40 kW power to the water. 1. Determine the exit velocity. 2. Determine the flow rate. 3. Determine the inlet velocity. Problem 268 A pump lifts water at the rate of 180 cfs to a height of 375 ft. above the water surface of the reservoir at a pipe friction loss of 27 ft. 1. Find the energy added by the pump.

2. Find the difference in elevation of the energy gradient at the tip of the nozzle and the water surface at the reservoir. 3. Find the power required if the pump efficiency 9s 88% and the velocity head is equal to 4 ft. Problem 269 3 A pump lifts water at the rate of 6 m /¿ s to a height of 120 m. and the friction loss in the pipe is 10 m.

1. Compute the energy added by the pump. 2. Compute the power output in kW. 3. What is the power in kW required if the pump efficiency is 90%? Problem 270 A turbine is located at an elevation of 200 m. below that of the surface of the water at intake. The friction loss in the pipeline leading to it is 8 m. and the turbine efficiency is 90%. 1. What is the energy extracted by the turbine. 2. Compute the input power delivered by the water to the turbine if the 3 flow is 3 m /sec in kW. 3 3. What will be the power delivered by the turbine if the flow is 3 m /sec in kW.

Problem 271 Oil (sp.gr = 0.82) enters a pump through a 20 cm. diameter pipe at 40 kPa. It leaves the pump at 125 kPa through a 15 cm. diameter pipe. If the flow rate is 75 liters/sec. 1. Find the rate at which energy is delivered to the oil by the pump in Jules/Newton. Assume section and discharge sides of the pump are at the same elevation. 2. Find the output hp of the pump. 3. If the efficiency of the pump is 82%, find the rating of the pump. Problem 272 The diameters of the suction and discharge pipes of a pump are 15 and 1cm. respectively. The discharge pressure is read by a gage at a point 1.5 m above the centerline of the pump and the suction pressure is read by a gage

0.6 m below the centerline. If the pressure gage reads 140 kPa and the suction gage reads a vacuum of 21 mmHg when gasoline is pumped at the rate of 35 liters/sec, (specific gravity of gasoline is 0.75) 1. Find the energy added by a pump. 2. Find the power delivered to the fluid in kW. 3. Find the required rating horsepower if the pump if it has an efficiency of 75%. Problem 273 During a flow of 500 liters, the gage pressure is +68 kPa in the horizontal 300 mm supply line of water turbine and a -41 kPa at a 450 mm section of the draft tube 2 m. below. Estimate the horsepower output of the turbine under such conditions assuming efficiency of 85%. 1. Compute the total head extracted by the turbine. 2. Compute the output horsepower of the turbine. 3. Assuming an efficiency of 85%, compute the horsepower input of the turbine. Problem 274 Water flows from an upper reservoir to a lower one while passing through a turbine as shown. Total length of pipe is 100 m with the diameter of 250 mm. Water flows at a rate of 150 liters/sec. neglecting minor losses and using Hazen Williams formula with c=120. 1. Compute the head loss of the pipe system. 2. Compute the total energy extracted by the turbine. 3. Compute the power generated by the turbine in kW, assuming unit 3 weight of water is 9.79 kN. m . Problem 275 Water is being discharged from a reservoir through a turbine as shown at a 3 rate of 20 ft /sec. total length of pipe is 270 ft. with a diameter of 36 in. using Hazen Williams Formula with C=120. 1. Compute the head loss in the pipe system. 2. Compute the total energy extracted by the turbine in order for the turbine to generate 100 hp.

3. What water-surface elevation is required in the reservoir in order for the turbine to generate 100 hp? Problem 276 3 The flow rate of water through the turbine shown is 0.20 m /sec and the pressures at points 1 and 2 are 150 kPa and -35 kPa.

1. Find the exit velocity at point 1 if it has diameter of 250 mm. 2. Compute the energy extracted by the turbine. 3. Compute the power generated by the turbine. Problem 277 A horizontal 600 mm diameter pipeline carries oil of specific gravity of 3 0.825 flowing at a rate of 0.44 m /sec. Each of the 4 pumps required along the line is the same, i.e, the pressure on the suction side and on the discharge side will be 60 kPa and 400 kPa, respectively. 1. Compute the head loss between the pump. 2. If the lost head at the discharge stated is 2 m for each 100 m of pipe, how far apart may the pumps be placed? 3. Compute the friction factor of the pipeline between pumps. Problem 278 During a test of centrifugal pump, a gage just outside the casing and on the 20 cm, suction pipe registered a pressure of 27.5 kPa less than the atmospheric. On the 15 cm discharge pipe another gauge indicated a pressure of 200 kPa above atmospheric. If a vertical distance of 1.0 m intervened between the pipe centers at the sections where the gauges were attached when pumping 57 liters/sec. compute the following: 1. The velocity of flow at the suction side. 2. The energy added by the pump. 3. The horsepower expected by the pump in useful work. Problem 279 Water is being discharged from a reservoir through a turbine as shown. 3 Assume unit of weight of water is 9.79 kN /m and c=120 for all pipes. Rate 3 of flow is 0.28 m /sec.

1. Determine the total head loss of the pipe. 2. Determine the energy extracted by the turbine to generate 56 kW of power. 3. Determine the elevation of the water surface in the reservoir that would be required for the turbine to generate 56 kW of power. Problem 280 Oil with specific gravity of 0.86 is flowing in a 450 mm diameter steel pipe line at a velocity of 1.20 m/s. Pumping stations for this pipeline are spaced 8 km. apart. 1. Compute the total head loss of the pipe in m if f = 0.015. 2 2. Compute the increase in head in kg/ m . 3. What should be the horsepower expected from each pump. Problem 281 Water is pumped from reservoir A at elevation 30 m through 1200 m of 600 on pipe to reservoir B at elevation 90 m. The pump is close to reservoir A and at the same elevation as A. A. hydraulic motor is placed in the pipeline at a point midway on the length of pipe, and at elevation 80 m. The motor delivers 56 hp, and is 80% efficient. With water delivery of 890 liters/sec and f = 0.02. 1. Determine the energy extracted by the hydraulic motor. 2. Determine the energy added by the pump. 3. What will be the power output of the pump? Problem 282 A 300 mm diameter pipe line 3000 m. long runs on a constant grade between two reservoirs of surface elevations 150 m and 120 m respectively. The flow rate through the line is inadequate and pump is installed to 3 increase the capacity of 0.17 m /s.

1. Assuming a Darcy “f” of 0.02, compute the head loss of the pipe. 2. Compute the total energy that the pump must supply. 3. Calculate the horsepower that must be delivered to the water to pump 3 the 0.17 m /s down the higher to lowest reservoir. Problem 283 You are asked to design a pump which is to supply fire flow to a hydrant by way of a 6” diameter ductile iron pipe with roughness coefficient f = 0.025, and is 800 feet long. Connect to the fire hydrant is a cotton-rubber lined 1 fire hose 2 2 inches in diameter (f = 0.018). The hose is 300 feet-long and 1 terminates in a nozzle with a tip diameter of 1 2 inches and C=Cv= 0.97,

C being coefficient of discharge and Cv is coefficient of velocity. The nozzle is at an elevation 25 feet higher than the pump. Assume a pressure loss in the hydrant of (2 psi). 1. When the flow is (250 gpm) what pressure in pounds per square inch must be maintained on the discharge side of the pump? 2. If the pressure on the suction side of the pump in the 6 inch diameter suction pipe is 8. What is the horsepower output of the pump? 3. What is the head loss in the 6” diameter ductile pipe? 4. What is the head loss in the 2.5” diameter hose? 5. What is the velocity head at the nozzle? Problem 284 A pump is discharging 12 liters/sec of water through 100 mm diameter smooth steel pipe. When the pressure on the discharge side of the pump is 700 kPa, the discharge pipe is at a point 540 m distant from the pump and 45 m higher in elevation. 1. 2. 3. 4.

What is the velocity of flow on the discharge side of the pump? Assuming f = 0.025, compute the head loss in the pipe. Compute the pressure expected in the discharge pipe. Problem 285

A pump draws water from reservoir A and lifts it to reservoir B as shown. The loss of head from A to 1 is 3 times the velocity head in the 150 mm pipe

and the loss of head from 2 to B is 20 times the velocity head in the 100 mm pipe. When the discharge is s20 liters/sec. 1. Compute the horsepower output of the pump in kilowatts. 2. Compute the pressure head at 1. 3. Compute the pressure head at 2. Problem 286 A fire pump delivers water through a 300 mm main to a hydrant to which is connected a cotton rubber-lined fire base 100 mm in diameter termination in a 25 mm nozzle. The nozzle is 2.5 m above the hydrant and is 16 m above the pump. Assuming frictional losses of 3 m. from the pump to the hydrant, 2 m. in the hydrant and 10 m from the hydrant to the base of the nozzle and a loss in the nozzle of 4% of the velocity head of the jet. 1. What vertical height can the jet be thrown if the gage pressure at the pump is 550 kPa. 2. Compute the total head loss. 3. Compute the discharge of water out of the nozzle in liter/s. Problem 287 A 20 hp suction pump operating at 70% efficiently draws water from a suction line whose diameter is 200 mm and discharges into air through a line whose diameter is 150 mm. The velocity in the 150 mm line is 3.6 m/s. If the pressure at point A in the suction pipe is 34 kPa below the atmosphere, where A is 1.8 m. below B on the 150 mm line. 1. Find the energy added by the pump. 2. Determine the maximum elevation above B to which water can be raised assuming a head loss of 3 m due to friction. 3. Find the pressure at B. Problem 288 A turbine is installed as shown in the figure. The gage at 1 us 80 kPa while 3 that of B it is -46 kPa. If the rate of flow is 0.48 m /sec. 1. Compute the total head loss extracted by the turbine. 2. Compute the input horsepower of the turbine. 3. If the efficiency of the turbine is 82%, compute its output hp. Problem 289

The 600 mm diameter pipe shown conducts water from reservoir A to a pressure turbine, which discharges through another 500 mm diameter pipe into tail race B. The loss of head from A to 1 is 5 times the velocity head in the pipe and the velocity head in the pipe. If the discharge is 700 liters/sec. 1. Compute the total head loss. 2. Compute the energy given up by the water to the turbine. 3. What horsepower is being given up by the water to the turbine? Problem 290 From a reservoir whose surface of elevation is at 30 m. water is pumped to an elevated reservoir at an elevation of 95 m. The total length of a 0.60 diameter suction pipe is 1500 m. and that of the 0.50 m diameter discharge pipe is 100 m. If the discharge is to be maintained at 480 L/sec. 1. Compute the total head loss using f = 0.02 and let minor losses be equal to 10% of major losses. 2. What is the energy added by the pump to the water? 3. What is the required horsepower of the pump? Problem 291 A pipeline with a pump leads to a nozzle as shown. 1. Find the flow rate when pump “P” develops on 24.4 m head. Assume head loss in 252 mm pipe expressed by 102 mm pipe is

5 v2 2g

while head loss in the

12 v 42 2g .

2. Find the pressure head at the suction side. 3. Find the velocity at the jet having a diameter of 75 mm. Problem 292 A concrete rectangular tank as shown in the figure has continuous inflow of 3

1.2 m /s and the same discharge exits to a 2 m. wide basin thru a 5- m. long reinforced barrel 0.90 by 0.90 m. in size. Using entrance loss coefficient Ke = 0.50, outlet loss coefficient due to sudden enlargement, Ke = 1.00, and the coefficient of roughness, n = 0.015. 1. Compute the velocity of flow inside the rectangular tank.

2. Compute the friction loss of the concrete rectangular tank. 3. Determine the required difference between the upstream and the downstream water surgace to allow the passage of the said flow. Problem 293 A flood control station is built to prevent sewage backflow during high tide. To reduce the energy consumption, gates were installed so that during low tide sewage flow freely through its gates. A typical cross-section of the station is shown. Assume head loss to be 1.20 m of sewage. 1. Compute the total energy output given by the pump to the system so that it will flow from left to right direction. 2. Compute the power input to the pump operating 75% efficiency if it is 3 to discharge 3 m /s of sewage. 3. Compute the maximum height of sea water at which the gate CD (6.5 m wide and 6.0 m high) will start to open. Neglect the weight of the gate and assume the surface at D to be frictionless. Problem 294 During a test of centrifugal pump, a gauge just outside the casing and on the 20 cm. suction pipe registered a pressure of 27.5 kPa less than the atmospheric. On the 15 cm. discharge pipe another gauge indicated a pressure of 200 kPa above atmospheric. If a vertical distance of 1.0 m intervened between the pipe enters at the sections where the gauges were attached. 1. Determine the velocity and the discharged pipe. 2. Determine the energy added by the pump. 3. What horsepower was expended by the pump in useful work when pumping 57 liters/sec?