# Jet Impinging on a Spring-Loaded Plate

## Problem Description

$\rho $ is fluid density. $Q$ is volumetric flowrate. $V$ is the jet velocity.

Volumetric flow of a jet of diameter d is Q = πd^{2}/4, where d is jet
diameter. Assuming a spring with a stiffness of k, the above force will displace the
plate by Δx = F/k.

To reduce the oscillations, the plate motion is critically damped using a linear
damper. The damping coefficient is set to c = 2(kM)^{1/2}, so the plate of
mass M approaches its equilibrium position without overshooting.

ρ [kg/m^{3}] |
µ [Pa.s] | V [m/s] | k [N/m] | c [N.s/m] | d [m] | M [kg] |
---|---|---|---|---|---|---|

1000 | 0.001 | 10 | 7068.58 | 531.74 | 0.03 | 10 |

## Numerical Setup

## Results

In Figure 2, the plate reaches a constant displacement of 0.0989m between 0.4s and 0.5s, very close to the analytical value of 0.01m. While the force applied to the plate has some oscillations, the time averaged force on the plate in 0.1s to 0.5s interval is equal to 69.94N. The analytical value of the impact force is equal to 70.68N.