Jet Impingement on a surface

Consider a jet with a cross section A_j at a speed v_j impinging on a solid surface at an angle $\theta$ as shown in Fig.3.29. It is required to calculate the normal force exerted on the surface.

Figure 3.29: Jet impinging on a surface

 

Let us consider the physics of the process first. As the jet impinges upon the surface, it splits into two parts. These move tangential to the surface. The normal component of the force however does act upon the surface and is to be countered for stability.

Prescribe x and y axes parallel and perpendicular to the surface and chose a control volume as shown. At the entry to the control volume we have the momentum in the y-direction equal to

$$\int_{Aj}v \rho~v_j cos\theta dA ~=~\rho~A_j~v_j~v_j~cos\theta~=~\dot{m} u_j cos\theta$$ (3.95)

At the solid surface velocity normal is zero and as such there is no normal momentum acting. The normal force acting upon the surface is given by Eqn.3.95.

(c) Aerospace, Mechanical & Mechatronic Engg. 2005
University of Sydney