Mechanics of Fluids

660 Fluid machines
in the impeller if 50% of the velocity head at outlet from the
impeller is recovered as static head in the volute.
13.14 The impeller of a centrifugal fan has an inner radius of 250 mm
and width of 187.5 mm; the values at exit are 375 mm and
125 mm respectively. There is no whirl at inlet, and at outlet
the blades are backward-facing at 70 ◦ to the tangent. In
the impeller there is a loss by friction of 0.4 times the kinetic
head corresponding to the relative outlet velocity, and in the
volute there is a gain equivalent to 0.5 times the kinetic head
corresponding to the absolute velocity at exit from the runner.
The discharge of air is 5.7 m 3 · s −1 when the rotational
speed is 84.8 rad · s −1 (13.5 rev/s). Neglecting the thickness of
the blades and whirl slip, determine the head across the fan
and the power required to drive it if the density of the air is
sensibly constant at 1.25 kg · m −3 throughout and mechanical
losses account for 220 W.
13.15 A centrifugal fan, for which a number of interchangeable
impellers are available, is to supply air at 4.5 m 3 · s −1 to
a ventilating duct at a head of 100 mm water gauge. For
all the impellers the outer diameter is 500 mm, the breadth
180 mm and the blade thickness negligible. The fan runs at
188.5 rad · s −1 (30 rev/s). Assuming that the conversion of
velocity head to pressure head in the volute is counterbalanced
by the friction losses there and in the impeller, that
there is no whirl at inlet and that the air density is constant at
1.23 kg · m −3 , determine the most suitable outlet angle of the
blades. (Neglect whirl slip.)
13.16 A centrifugal pump which runs at 104.3 rad · s −1 (16.6 rev/s) is
mounted so that its centre is 2.4 m above the water level in the
suction sump. It delivers water to a point 19 m above its centre.
For a flow rate of Q (m 3 · s −1 ) the friction loss in the suction
pipe is 68Q 2 m and that in the delivery pipe is 650Q 2 m. The
impeller of the pump is 350 mm diameter and the width of
the blade passages at outlet is 18 mm. The blades themselves
occupy 5% of the circumference and are backward-facing
at 35 ◦ to the tangent. At inlet the flow is radial and the
radial component of velocity remains unchanged through the
impeller. Assuming that 50% of the velocity head of the water
leaving the impeller is converted to pressure head in the volute,
and that friction and other losses in the pump, the velocity
heads in the suction and delivery pipes and whirl slip are
all negligible, calculate the rate of flow and the manometric
efficiency of the pump.
13.17 A single-stage centrifugal pump is to be used to pump water
through a vertical distance of 30 m at the rate of 45 L · s −1 .
Suction and delivery pipes will have a combined length of 36 m
and a friction factor f of 0.006. Both will be 150 mm diameter.