Answer:
F = 8552.7N
Explanation:
We need first our values, that are,
[tex]V_{jet} = 40m/s\\V_{Plate} = 10m/s \\D = 11cm[/tex]
We start to calculate the relative velocity, that is,
[tex]V_r = V_{jet}-V_{plate}\\V_r = (40)-(10)\\V_r = 30m/s[/tex]
With the relative velocity we can calculate the mass flow rate, given by,
[tex]\dot{m}_r = \rho A V_r[/tex]
[tex]\dot{m}_r = (1000)(30) \frac{\pi (0.11)^2}{4}[/tex]
[tex]\dot{m}_r = 285.09kg/s[/tex]
We need to define the Force in the direction of the flow,
[tex]\sum\vec{F} = \sum_{out} \beta\dot{m}\vec{V} - \sum_{in} \beta\dot{m} \vec{V}\\[/tex]
[tex]F = \dot{m}V_r[/tex]
[tex]F = (285.09Kg/s)(30)[/tex]
[tex]F = 8552.7N[/tex]
