# Fluid dynamics, confined flow

1. Apr 11, 2010

### J Hill

1. The problem statement, all variables and given/known data
Air flows from a hole of diamter .03 m in a flat plate as shown in the figure. A circular disk of diameter D = .15 m is placed a distance h from the lower plate. The pressure in the tank is maintained at 1 kPa. Determine the flowrate as a function of h, ignoring viscous effects and elevation changes, and the flow exits radially from the circumfrence of the circular disc with uniform velocity.

Figure (bad as it may be)
oo______ D = 0.15 m
<_-_ _-_> |h
oooo|
ooo/
oo/ 1kPa
= P0
(the bottom part is symmetric)

2. Relevant equations

Bernouli's equation: P + 1/2 \rho v^2 = constant along stream line
Flowrate: Q = A*v

3. The attempt at a solution

Okay, as the air flows passed the edge of circular disc the pressure should be the same as atmospheric pressure, so it should be possible to use Bernouli's equation:
$$P_0 = 1/2 \rho v^2$$
or
$$v = \sqrt{2*P0\rho}$$

The area that the fluid flows out is:
$$A = \pi D h$$

So
$$Q = \pi D \sqrt{2*P_0/\rho} h$$

I'm not sure if this is right, or if this only applies for small values of h.

Last edited: Apr 11, 2010