Mechanics of Fluids

Losses at valves, etc. are estimated to total 2.4 times the velocity
head in the pipes. The basic design of pump has a specific
speed of 0.465 rad (0.074 rev), forward-curved impeller blades
with an outlet angle of 125 ◦ to the tangent and a width of
impeller passages at outlet equal to one-tenth of the diameter.
The blades themselves occupy 5% of the circumference. If a
manometric efficiency (neglecting whirl slip) of 75% may be
expected, determine a suitable impeller diameter.
13.18 The impeller of a centrifugal pump has an outer diameter of
250 mm and an effective outlet area of 17 000 mm 2 . The
outlet blade angle is 32 ◦ . The diameters of suction and discharge
openings are 150 mm and 125 mm respectively. At
152 rad · s −1 (24.2 rev/s) and discharge 0.03 m 3 · s −1 the pressure
heads at suction and discharge openings were respectively
4.5 m below and 13.3 m above atmospheric pressure, the
measurement points being at the same level. The shaft power
was 7.76 kW. Water enters the impeller without shock or
whirl. Assuming that the true outlet whirl component is
70% of the ideal, determine the overall efficiency and the
manometric efficiency based on the true whirl component.
13.19 The following duties are to be performed by rotodynamic
pumps driven by electric synchronous motors, speed
100π/n rad · s −1 (= 50/n rev/s), where n is an integer:
(a) 14 m 3 · s −1 of water against 1.5 m head; (b) oil (relative
density 0.80) at 11.3 L · s −1 against 70 kPa pressure; (c) water
at 5.25 L · s −1 against 5.5 MPa. Designs of pumps are available
with specific speeds of 0.20, 0.60, 1.20, 2.83, 4.0 rad.
Which design and speed should be used for each duty?
13.20 During a laboratory test on a water pump appreciable cavitation
began when the pressure plus velocity head at inlet was
reduced to 3.26 m while the total head change across the
pump was 36.5 m and the discharge was 48 L · s −1 . Barometric
pressure was 750 mm Hg and the vapour pressure of water
1.8 kPa. What is the value of σc? If the pump is to give the
same total head and discharge in a location where the normal
atmospheric pressure is 622 mm Hg and the vapour pressure
of water 830 Pa, by how much must the height of the pump
above the supply level be reduced?
13.21 A large centrifugal pump is to have a specific speed of 1.15 rad
(0.183 rev) and is to discharge liquid at 2 L · s −1 against a
total head of 15 m. The kinematic viscosity of the liquid may
vary between 3 and 6 times that of water. Determine the
range of speeds and test heads for a one-quarter scale model
investigation of the full-size pump, the model using water.
13.22 A 500 mm diameter fluid coupling containing oil of relative
density 0.85 has a slip of 3% and a torque coefficient
of 0.0014. The speed of the primary is 104.7 rad · s −1
Problems 661