skmm2323 Turbomc Tutorial PDF

FACULTY OF MECHANICAL ENGINEERING
UNIVERSITI TEKNOLOGI MALAYSIA
SKMM 2323 Mechanics of Fluid II Turbomachinery
1. A water pump is used to pump water from one large reservoir to another large reservoir that is
at a higher elevation. The free surfaces of both reservoirs are exposed to atmospheric pressure,
as sketched in Fig. P14-41. The dimensions and minor loss coefficients are provided in the figure.
The pump’s performance is approximated by the expression Havailable = H0 − aQ2 , where shutoff
head H0 = 24.2 m of water column, coeeficient a = 0.0678 m/(l/min)2 , Havailable is in units of
meters of water column, and the capacity Q is in units of liters per minute. Estimate the capacity
delivered by the pump.
z2 − z1 = 7.85 m (elevation difference)

D = 2.03 cm (pipe diameter)
K L,entrance = 0.50 (pipe entrance)
K L,valve = 17.5 (valve)
K L,exit = 1.05 (pipe exit)
L = 176.5 m (total pipe length)
ǫ = 0.25 mm (pipe roughness)
[11.6 litres/min]
2. Consider the pump in the above problem.

(a) The pump diameter is 1.80 cm, and it operates at N = 4200 rpm. Nondimensionalize the
pump performance curve, i.e., plot K H versus K Q . Show sample calculations of K H and K Q
at Q = 14.0 litres/min. Use
Q gH
KQ = and KH = .
ND3 N 2 D2
(b) Calculate the pump specific speed at the best efficiency point (BEP) for the case in which the
BEP occurs at 14.0 litres/min. Provide answers in dimensionless form. What kind of pump
is it?
[centrifugal]
3. Len is asked to design a small water pump for an aquarium. The pump should deliver
18.0 litres/min of water at a net head of 1.6 m at its best efficiency point. A motor that spins
at 1200 rpm is available.
(a) What kind of pump (radial/centifugal, mixed, or axial) should Len design? Show all your
calculations and justify your choice. Estimate the maximum pump efficiency Len can hope
for with this pump.
[centrifugal, 75%]
(b) Suppose the pump is modified by attaching a different motor, for which the rotational speed
is half that of the original pump. If the pumps operate at homologous point (namely, at
the BEP) for both cases, predict the volume flow rate and net head of the modified pump.
Calculate the pump specific speed of the modified pump, and compare to that of the original
pump. Discuss.
4. A group of engineers is designing a new hydroturbine by scaling up an existing one. The existing
turbine (turbine A) has diameter D A = 1.50 m, and spins at NA = 150 rpm. At its best efficiency
point, Q A = 162 m3 /s, H A = 90.0 m of water, and PA = 132 MW. The new turbine (turbine B)
will spin at 120 rpm, and its net head will be HB = 110 m. Calculate the diameter of the new
turbine such that it operates most efficiently, and calculate Q B and PB .
[2.07 m, 342 m3 /s, 341 MW]
5. A centrifugal pump discharges 0.13 m3 /s when running at a speed of 1450 rpm. Head developed
is 30 m. Impeller diameter and width at the outlet are 30 cm and 5 cm, respectively. Hydraulic
efficiency is 77%. Find the blade angle at the outer periphery of the impeller.
[24◦ 42′ ]
6. A centrifugal pump works against a head of 25 m and discharges 0.22 m3 /s while running at
1000 rpm. Velocity of flow at the outlet is 2.8 m/s and the outlet angle of the blade is 30◦ . De-
termine the diameter and the width of the impeller at the outlet. Take hydraulic efficiency as
78%.
[38.8 cm, 6.4 cm]
7. A centrifugal pump delivers 50 litres of water per second to a height of 15 m through a 20 m long
pipe. Diameter of the pipe is 14 cm. Overall efficiency is 72% and the coefficient of friction 0.015.
Determine the power needed to drive the pump.
[13.73 kW]
8. The flow through a Pelton wheel is 250 litres per second under a head of 300 m. Calculate the
power produced and the hydraulic efficiency if the mean bucket speed is 35 m/s and the buckets
deflect the jet through an angle of 160◦ . Take cv = 0.97.
[669 kW, 91%]
9. Each Pelton turbine at a hydro-power station works under a head of 940 m and produces 8000 kW
of power. If the turbine runs at 600 rpm, find
(a) diameter of the jet,
(b) mean diameter of the wheel,
(c) ratio of the wheel diameter to the jet diameter.
Take cv = 0.98, U/v j = 0.46 and η = 0.89.
[96.5 mm, 1.99 m, 20.6]
10. Calculate the number of jets required for a Pelton wheel to develop 10 MW under a head of 370 m
when running at 500 rpm. Ratio of the wheel diameter to the jet diameter is 12. Assume suitable
values of coefficient of velocity, speed ratio and the overall efficiency.
[3]
11. An inward-flow reaction turbine produces 130 kW while working under a head of 20 m. The
discharge through the turbine is 0.75 m3 /s, and is radial at the outlet. The diameters at the inlet
and outlet are 60 cm and 45 cm, respectively. Take radial velocity at the outlet as 3 m/s, width of
the wheel constant and speed of the runner 480 rpm. Find
(a) overall and hydraulic efficiencies,
(b) inlet angle of guide vane and runner blades.
[88.4%, 97.7%, 10◦ 2′ , 43◦ 31′ ]
12. A Francis turbine has a constant flow velocity of 2.5 m/s through the turbine and the discharge is
radial. Width of the turbine at the inlet is 22 cm and the guide vane angle is 15◦ to the tangent of
the wheel. Diameters of wheel at the inlet and the outlet are 0.8 m and 0.6 m, respectively, which
runs at 200 rpm. Find
(a) absolute velocity of water at the inlet,
(b) runner blade angles,
(c) power developed,
(d) hydraulic efficiency of turbine.
[9.66 m/s, β1 =69◦ 12′ , β2 =21◦ 42′ , 109 kW, 96.2%]

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FACULTY OF MECHANICAL ENGINEERING

UNIVERSITI TEKNOLOGI MALAYSIA

SKMM 2323 Mechanics of Fluid II Turbomachinery

z2 − z1 = 7.85 m (elevation difference)

2. Consider the pump in the above problem.

[2.07 m, 342 m3 /s, 341 MW]

[38.8 cm, 6.4 cm]

[669 kW, 91%]

[96.5 mm, 1.99 m, 20.6]

[88.4%, 97.7%, 10◦ 2′ , 43◦ 31′ ]

[9.66 m/s, β1 =69◦ 12′ , β2 =21◦ 42′ , 109 kW, 96.2%]

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