Calculation of pressure in a pipeline derived from volume flow rate.

[Bulldogio]

Is it possible to derive the pressure of air flowing through a pipeline from the volume flow rate and the diameter of the pipe. For instance pipe I.D. = 150mm and volume flow rate = 0.3m³/sec.
I have looked at Bernoulli's eqn and the continuity eqn and hence come to the conclusion that the pressure is dependant on the input to the line. I have no other data for this query other than I can tell you the media is air and the pipe is situated in a tunnel.
Please help, for I am getting a little bit frustrated.

 

[vzeos]

You need more information. The square of the flowrate of a gas flowing in a pipe is proportional to the difference of the square of the absolute inlet pressure and the square of the absolute outlet pressure, Q_b² [∝] (P₁²- P₂²). Note that the pressure difference is not constant for any particular flowrate. You would need to know one pressure, the pipe diameter, pipe length and flowrate to estimate the other pressure.

If you get involved in pipe calculations for gases, the following equations may be useful to you.

General Gas flow equation:
Q_b= 234.8 (T_b /P_b )([√]1/f){(P₁²- P₂²)/( G L Z_avgT_avg)}^1/2 D^2.5

General Gas flow equation with elevation correction:
Q_b= 234.8 (T_b /P_b )([√]1/f){(P₁²- P₂² - 0.0375 G dX (P_avg²/Z_avgT_avg))/( G L Z_avgT_avg)}^1/2 D^2.5
Where:
Q_b=scfh
T_b=base temp, deg R
P_b=base pressure, psia
[√]1/f = transmission factor (f= Darcy-Weisbach friction factor)
P₁ and P₂ = inlet and outlet pressure, psia
D=diameter, inches
G= gravity relative to air
dX=elevation change, feet
P_avg=average pressure, psia
T_avg=average temperature, deg R
L=Length, feet
Z_avg=average compressibility

Colebrook (Darcy-Weisbach)
1/[√]f= -2Log{(k_e/3.7D)+(2.51/N_Re)1/[√]f}