fluid_mechanics

650 Chapter 12 ■ Turbomachines
E XAMPLE 12.1
Basic Difference between a Pump and a Turbine
GIVEN The rotor shown in Fig. E12.1a rotates at a constant
angular velocity of v 100 rads. Although the fluid initially
approaches the rotor in an axial direction, the flow across the
blades is primarily outward 1see Fig. 12.2a2. Measurements
indicate that the absolute velocity at the inlet and outlet are
V 1 12 ms and V 2 15 ms, respectively.
FIND Is this device a pump or a turbine?
SOLUTION
To answer this question, we need to know if the tangential component
of the force of the blade on the fluid is in the direction of
the blade motion 1a pump2 or opposite to it 1a turbine2. We assume
that the blades are tangent to the incoming relative velocity and
that the relative flow leaving the rotor is tangent to the blades as
shown in Fig. E12.1b. We can also calculate the inlet and outlet
blade speeds as
and
U 1 vr 1 1100 rads210.1 m2 10 ms
U 2 vr 2 1100 rads210.2 m2 20 ms
With the known, absolute fluid velocity and blade velocity at
the inlet, we can draw the velocity triangle 1the graphical representation
of Eq. 12.12 at that location as shown in Fig. E12.1c.
Note that we have assumed that the absolute flow at the blade
row inlet is radial 1i.e., the direction of V 1 is radial2. At the outlet
we know the blade velocity, U 2 , the outlet speed, V 2 , and the relative
velocity direction, b 2 1because of the blade geometry2. Therefore,
we can graphically 1or trigonometrically2 construct the outlet
velocity triangle as shown in the figure. By comparing the velocity
triangles at the inlet and outlet, it can be seen that as the fluid flows
across the blade row, the absolute velocity vector turns in the direction
of the blade motion. At the inlet there is no component
of absolute velocity in the direction of rotation; at the outlet this
component is not zero. That is, the blade pushes and turns the
fluid in the direction of the blade motion, thereby doing work on
the fluid, adding energy to it.
This device is a pump.
(Ans)
β = 60°
2
(2)
(2)
r 2 = 0.2m
U 2 = 20 m/s
(1)
ω = 100 rad/s
r 1 = 0.1m
(1)
U 1 = 10 m/s
Blade
motion
(2) 60°
W 2
(1)
Blade
W 1
(a)
+
(b)
U 2 = 20 m/s
V 2 = 15 m/s
30°
W 2
= 60° β 2
Outlet
U 1
V 1
Radial
Circumferential
U 1 = 10 m/s
Known quantities
shown in color
V 2
U 2
W 2
W 1
ω
V 1 = 12 m/s
W 1
Inlet
(c)
F I G U R E E12.1
(d)