# Under pressure -- flow rate through multiple holes in a pipe

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1. Nov 30, 2014

### Bruce Center

I am looking at air system that is under a constant pressure of 350 mbar into a pipe that has 40 - 2 mm round holes. Is there a formula that I can use to calculate the total volume of air nm3/hr that will escape the system?
Let's just say the air temp is constant.
Can anyone help with this?

2. Nov 30, 2014

### jack action

On this website, you have the equations to define the velocity of your fluid based on your known pressure drop in the section Static, dynamic and total pressure, flow velocity and Mach number ($\gamma$ = 1.4 for air). You will have to do trial and error to find it since M = v / c (where c = 343 m/s at 20°C, see speed of sound for air). The density $\rho$ is defined in equation (8) based on Mach number where $\rho_t = \frac{P_t}{RT_t}$ where $P_t$ & $T_t$ are the pressure (in Pa) and temperature (in K) of your air when at rest (may be your initial pressure and ambient temperature if your air inside the pipe can be assumed to be immobile) and $R$ = 287 J/kg/K for air.

Then you multiply that velocity by your total exit area of your holes to get your volumetric flow rate. The velocity must in m/hr and the area in m² to get the answer in m³/hr.