Jet on a fixed inclined plate: force component normal to the original flow A water jet of velocity V and area a strikes a fixed flat plate inclined at angle θ to the jet direction. Find the force exerted by the jet on the plate in the direction <em>perpendicular to the initial jet</em> (normal to flow). Choose the correct expression.

Given

• Jet: speed V, area a, density ρ → mass flow rate ṁ = ρ a V.
• Plate: fixed, inclined at θ to jet.

Approach
Take x along the jet and y normal to the jet. The plate eliminates the normal-to-plate velocity component; in x–y, the outgoing flow has zero y-component.

Step-by-step
Incoming momentum flux in y = ṁ (V sin θ) = ρ a V · V sin θ = ρ a V^2 sin θ.Outgoing momentum flux in y = 0 (fixed plate, flow slides along the plate).Force on plate in +y (on fluid in −y) = Δ(momentum flux in y) = ρ a V^2 sin θ.

Checks
θ = 0° ⇒ F = 0 (plate parallel to flow) ✔θ = 90° ⇒ F = ρ a V^2 (plate normal to flow) ✔

Final Answer
F = ρ a V^2 sin θ