Question

A constant-velocity horizontal water jet from a stationary nozzle impinges normally on a vertical flat plate that rides on a nearly frictionless track. As the water jet hits the plate, it begins to move due to the water force. As a result, the acceleration will _____.

Answer 1

Answer:

a = ½ ρ A/M   v₁²

Explanation:

This is a problem of fluid mechanics, where the jet of water at constant speed collides with a paddle, in this collision the water remains at rest, we write the Bernoulli equation, we will use index 1 for the jet before the collision the index c2 for after the crash

           P₁ + ½ ρ v₁² + ρ g h₁ = P₂ + ½ ρ v₂² + ρ g h₂

in this case the water remains at rest after the shock, so v₂ = 0, as well as it goes horizontally h₁ = h₂

          P₁-P₂ = ½ ρ v₁²

         ΔP = ½ ρ v₁²

let's use the definition of pressure as a force on the area

         F / A = ½ ρ v₁²

         F = 1/2 ρ A v₁²

the density is

          ρ = m / V

the volume is

           V = A l

           F = ½ m / l v₁²

knowing the force we can focus on the acceleration of the mass palette M

         F = M a

         a = F / M

          a = ½ m/M  1/l   v₁²

           

as well it can be given depending on the density of the water

          a = ½ ρ A/M   v₁²