Properties We take the density of water to be 1000 kg/m3.
Analysis (a) We take the vertical plate on the frictionless track as the control volume, and the direction of flow as the positive direction of x axis. The mass flow rate of water in the jet is
m& = ρVA = (1000 kg/m3 )(18 m/s)[π (0.05 m)2 / 4] = 35.34 kg/s
The momentum equation for steady one-dimensional flow in the x (flow) direction reduces in this case to Σ =Σ −Σ
out in
F mV mV
r
&
r
&
r
β β → FRx = −m& iVi → FRx = −m&V
where FRx is the reaction force required to hold the plate in place. When the plate is released, an equal and
opposite impulse force acts on the plate, which is determined to
636 N
1 kg m/s
(35.34 kg/s)(18 m/s) 1 N 2 plate =
⋅
F = −FRx = m&V =
Then the initial acceleration of the plate becomes