# Plate floating on oil - linear momentum equation

1. Dec 2, 2012

### Pietair

1. The problem statement, all variables and given/known data
1: Determine the wall shear stress that acts at the lower side of the plate.
2: Determine the force Fx that is needed to give the plate a speed of u = 1m/s.
3: Determine the speed V, that is leaves an air jet that blows against the plate and which creates the same force Fx.

Question 1 and 2 were easy to solve, but I have got a problem with the third question.

2. Relevant equations
Linear momentum equation: $$\sum \vec{V}_{out} \rho_{out} A_{out} V_{out}-\sum \vec{V}_{in} \rho_{in} A_{in} V_{in}=\sum F$$

3. The attempt at a solution
The left part of the linear momentum equation is easy to find. However, I don't understand which forces I have to include when applying the linear momentum equation in the x-direction.
I know that I have to include a force -Fx, which is the force exerted by the plate on the control volume (which is the reaction force of the force exerted by the fluid on the plate).
But in the answer sheet they do not include the pressure force exerted on the left side of the control volume, which I think should be P_{atm} * the left area of the control volume (because the pressure in the air jet is simply P_{atm}. Why isn't this pressure force on the control volume included?

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