Question

1. The turbine of a hydrostatic plant is driven by a falling head of water from a falling head of water from a source 30 m high up through a 600 mm penstock flowing full.
A. Evaluate the theoretical velocity of water as it hits the turbine blades in m/sec.
B. Evaluate the theoretical discharge of water in m³/s.
C.If the turbine is only 70% efficient, estimate the horsepower available from it..

2. Reservoir A supplies water to a nozzle having a diameter of 80 mm which is discharge water 40 m below the reservoir water level at a velocity of 24m/s
A. Determine the loss of head in the pipeline.
B. Determine the horsepower produced by the jet.
C. Determine the efficiency of the nozzle.

3. The diameter of a pipe carrying water changes gradually from 150 mm at A to 450 mm at B. A is 5 m lower than B. If the pressure at A is 70 kPa and at B is 50 kPa when 150 liters/ sec is flowing.
A. Determine the direction of flow
B. Determine the frictional loss between two points

4. Reservoir A and B have elevations of 100 m and 160 m respectively. A pump is installed near reservoir A to pump the water from A to B. The rate flow in the pipe is 650 liters/sec. If the head loss in the pipeline is 8.22 m, compute the horsepower required to pump the water to B.

5. A reservoir A contains water at an elevation of 45 m and a 50 mm pipe line leads downhill from the reservoir and discharges into air at B at an elevation 0. If the loss of head between the reservoir A and B is 43.5 m compute the discharge flowing in the pipe.

6. A turbine is located at an elevation 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%. What will be the power delivered by the turbine if the flow is 3 m³/ sec in kW?

7. Water is discharged through a nozzle having a diameter of jet 100 mm at a velocity of 60 m/s at a point 240 m below the reservoir.
A. Compute the total headloss.
B. Compute the horsepower produced by the jet.
C. Compute the power lost in friction.

Answer 1

Ans 1-A) We know, theoratical velocity of water (V) =

where, H = Height of falling of water = 30 m

=> V =

=> V = 24.26 m/s

Ans 1-B) We know,

Flow rate (Q) = Area x velocity

Area of pipe = (/4)() = 0.2826 sq.m

=> Q = 0.2826 x 24.26

=> Q = 6.855 /s

Ans 1-C) We know,

Power delivered by turbine = g Q H

where, = water density = 1000 kg/m3

= efficiency = 70%

=> P = 1000 x 9.81 x 6.855 x 30 x 0.70

=> P = 1412198 W or 1893 hp

.

Ans 2-A) Apply Bernoulli between point 1 and 2 located at water surface elevation of reservoir and just outside nozzle respectively,

P1/ + /2g + Z1 = P2/ + /2g +Z2 + Hf

Since, both points are open to atmosphere, pressure is only atmospheric , hence gauge pressure P1 = P2 = 0

Velocity at surface is negligible so V1 =0

Elevation difference (Z1- Z2) = 40 m

Velocity at exit (V2) = 24 m/s

Hf is head loss due to friction

Putting values,

0 + 0 + 40 = 0 + /(2 x9.81) + Hf

=> 40 = 29.35 + Hf

=> Hf = 10.65 m

Hence, head loss in pipeline is 10.65 m

.

Ans 2-B) Horsepower produced by jet =   g Q H / 746

Flow rate (Q) = Area x velocity

=> Q = (/4)() x 24 = 0.12 m3/s

=> Horsepower produced = 1000 x 9.81 x 0.12 x 40 / 746 = 63.12 hp

.

Ans 2-C) We know, nozzle efficiency = Actual discharge / Theoratical discharge

Theoratical discharge = area x theoratical velocity

=> Theoratical discharge=  (/4)() x = 0.14 m3/s

=> Efficiency = 0.12 / 0.14

=> Efficiency = 0.857 or 85.7%