An axisymmetric jet of water strikes a wall at right angles and spreads out over it.
speed v and cross-section c.
find the force on the wall by momentum integral equation
Hello szpengchaoI'm not entirely sure what you mean by 'momentum integral equation'. In a problem like this, you need to use the principle that
Force = rate of change of momentum
Since the jet hits the wall at right angles, the volume of water hitting the wall in unit time = $\displaystyle cv$. So, if the density of water is $\displaystyle \rho$, the mass of water hitting the wall in unit time = $\displaystyle \rho cv$. (If $\displaystyle \rho = 1$, then obviously this mass is simply $\displaystyle cv$.)
Since the water spreads out across the wall, it doesn't bounce back. So all its momentum is lost. And therefore the momentum lost in unit time $\displaystyle = \rho cv \times v = \rho cv^2$.
This is therefore the rate of change of the momentum of the water, and therefore the force exerted by the wall on the water. By Newton's Third Law, this is then the force exerted by the water on the wall.
Grandad