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:
[tex]\dot{m} = \rho \dot{V}[/tex]
Where,
[tex]\rho =[/tex] Density of water
[tex]\dot{V} =[/tex] Volumetric flow rate
Replacing our values we have
[tex]\dot{m} =1000*0.09[/tex]
[tex]\dot{m} = 90Kg/s[/tex]
Calculate the force acting on the shaft by using the moment equation for steady one-dimensional flow,
[tex]\sum \vec{F} = \sum \limit_{out} \beta \dot{m} \vec{V} - \sum_{in} \beta \dot{m} \vec{V}[/tex]
[tex](-F_R)_x = -\beta \dot{m}V[/tex]
Where
[tex]\beta[/tex]=momentum flux Correction factor
V = Velocity
Replacing we have then
[tex]\beta = 1[/tex]
[tex]\dot{m} = 90kg/s[/tex]
[tex]V = 3m/s[/tex]
[tex]-(F_R)_x = (1\times 90\times 3)[/tex]
[tex](F_R)_x = 270N[/tex]
Therefore the force acting on the shaft is 270N
