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 = . So, if the density of water is , the mass of water hitting the wall in unit time = . (If , then obviously this mass is simply .)

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 .

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