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Analysis of Centrifugal Pumps (continued)

Summary: (Continued)

Key concept: The principle of conservation of energy can be used to determine the change in

pressure between the entrance to the vane (station 1) and the exit from the vane (station 2).

Conservation of Energy

p₁/ρg + V₁² /2g + z₁ + h_s = p₂/ρg + V₂² /2g + z₂ + h_L (ft or m)

where h_s is positive for a pump (adds energy to fluid)

and h_s is negative for a turbine (extracts energy from the fluid)

h_L is the head loss associated with the pump or turbine

For an ideal pump the head loss is zero.

Change in elevation is generally negligible. i.e z₁ ≈ z₂

Key Points:

The pump adds energy to the fluid. The energy at the entrance to the leading edge of the vane

plus the energy added by the pump equals the energy at the trailing edge of the vane plus

any head loss due to friction.

Each of the speeds (magnitude of velocities) in conservation of mass, of angular momentum, and

of energy are absolute values as measured in an inertial frame.

As the impeller rotates, fluid is sucked in through the eye of the casing and flows outward radially

where it strikes the leading edge of the vane.

The external shaft torque drives the impeller of the pump causing it to rotate. (ω)

The head loss due to friction from the entrance of fluid at the leading edge of the vane to the exit

at the trailing edge of the vane is considered negligible for an "ideal" pump.

Vector plots showing the tangential components of the fluid velocity, V_t1, at the entrance and

V_t2, at the exit are essential in calculating the shaft torque.