Question

Water enters a centrifugal pump axially at atmospheric pressure at a rate of 0.09 m3/s and at a velocity of 3 m/s, and it leaves in the normal direction along the pump casing. Determine the force acting on the shaft (which is also the force acting on the bearing of the shaft) in the axial direction. Take the density of water to be 1000 kg/m3.

Answer 1

To develop this problem it is necessary to apply the concepts related to Mass Flow, as a unit dependent on density and volumetric flow rate, as well as apply the sum of Forces on the flow. We will start by determining the mass flow:

$\dot{m} = \rho \dot{V}$

Where,

$\rho =$ Density of water

$\dot{V} =$ Volumetric flow rate

Replacing our values we have

$\dot{m} =1000*0.09$

$\dot{m} = 90Kg/s$

Calculate the force acting on the shaft by using the moment equation for steady one-dimensional flow,

$\sum \vec{F} = \sum \limit_{out} \beta \dot{m} \vec{V} - \sum_{in} \beta \dot{m} \vec{V}$

$(-F_R)_x = -\beta \dot{m}V$

Where

$\beta$=momentum flux Correction factor

V = Velocity

Replacing we have then

$\beta = 1$

$\dot{m} = 90kg/s$

$V = 3m/s$

$-(F_R)_x = (1\times 90\times 3)$

$(F_R)_x = 270N$

Therefore the force acting on the shaft is 270N