Problems (cont.) Pb 15.4.1 A model centrifugal pump has a scale ratio of I:15. The model tested at 3600 rpm, delivered 0.10 m/s of water at a head of 40 m with an efficiency of 80 percent. Assuming the prototype has an efficiency of 88 percent, what will be its speed, capacity, and power requirement at a head of 50 m? Solution
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- It is proposed to build a three- stage centrifugal pump to deliver 4000 kg/min of water at a speed of 900 rpm under a total manometric head of 70 m. The vanes are to be radial at inlet and are to be curved backwards at exit at an angle of 45°. Assuming manometric efficiency of 84% and overall efficiency of 75% and considering that vane thickness accounts for 8% of circumferential area. The velocity of flow may be assumed constant at 2.5 m/sec. The h.p. input necessary is ؟A centrifugal pump discharging 10 lps against 25 m of head and operating with an efficiency of 60% requires 4.1 kW at 1000 rpm. What is the theoretical discharge if the speed is increased to 1500 rpm assuming the efficiency remains constant? What is the theoretical head and kW at 1500 rpm?5. Water is pumped 14.5 km from a reservoir at elevation 30 m to another reservoir at elevation 70 m. The steel pipeline connecting the reservoirs has a nominal diameter of 1400 mm (the actual inside diameter is 1372 mm) with C = 90. If the flow is 1.18 m3/s, the pumping efficiency is 82%, and electricity costs $0.14/kWh. Assuming that the density of water is 1000 kg/m3, what will be the monthly power bill? Sketch the hydraulic and energy grade lines.
- Explain the relationship between efficiency n ,head H, inflow power Pi and the best efficiency point (BEP) of a centrifugal pump.What is the required pump power (Pa) for the system below? The source reservoir is on the right side of the figure The outflow is released as a water jet to the atmosphere (on the left) Discharge rate is 0.11 m3/s Pipe total length is 180 m Pipe diameter is 0.2 m Friction factor (f) is 0.01 Minor losses are negligibleCHOOSE ONE: 25 KiloWatt 169 KiloWatt 269 KiloWatt 112 KiloWattCompute the minimum water horsepower of a pump needed to pump-out water at a rate of 300 gpm with a total head of 6 m. The pump efficiency is about 60%.
- 9.The pump shown delivers 115 li/s of oil, sg = 0.84, toreservoir D at elevation 72 m. The energy lost in thesuction line is 3.2 J/N and in the discharge line is 7.6 J/N. a.Compute the total head added by the pump. b.How many kW does the pump supply the system? c.If the pump is 85% efficient, how much power does it need?6. A centrifugal pump discharging 900 gpm and operates at 1800 rpm against a head of 120 feet has a power output of 30 hp. If the pump is to operate at 1200 rpm assuming efficiency remains constant. Determine the new discharge in gpm, the head and power.Q1) If the flow rate through a 10 cm diameter wrought iron pipe is 0.04 m3/s, and the difference in elevation H of the two reservoirs is 77. Calculate the power of the pump. Assume the pump efficiency is 85%.
- A pump is attached to a fire hydrant, where it is desired to produce a jet that rises to a maximum height of 40 m and delivers water at a rate of 100 L/s. At the attachment location, the diameter is 100 mm and the pressure is estimated as 150 kPa. The discharge nozzle has a diameter of 80 mm and is inclined at an angle of 50 degrees to the horizontal. If friction losses are neglected, estimate the head that must be added by the pump to achieve the desired objective. The path of the water jet is parabolic.A small pump serving as model, when tested in laboratory using water at 3,600 rpm, delivered 3.0 cfs at a head of 125 ft. If the efficiency of this model pump is 84 %. Predict the horsepower input to the prototype pump if it is to develop the same head as model pump and the model pump has a scale ratio of 1 : 10. Assume the efficiency of the prototype pump is 90 %.Two reservoirs A and B have elevations of 250m and 100m respectively. It is connected by a pipe having a diameter of 250mm and a length of 100m. A turbine is installed at point in between reservoirs A and B. If C = 120, compute the following if the discharge flowing in the pipeline is 150 liters/sec. Compute the power generated by the turbine.