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I was wondering how I can calculate the velocity of gas through a pipe.

The gas, assuming ideal behavior, in a pipe (cylinder) of volume of 222.4 L has a pressure of 1.95 atmospheres and a density of 2.25 kg/m$^3$. Knowing that there will be turbulent flow, the equation,

$$V\ =\ \sqrt\frac{2\Delta P}{{\rho (4f\frac{\Delta x}{D}\ -\ 1)}}$$

can be used. However, because this is a pipe with no change in volume, the pressure should remain even, so can I plug in 2.25 kg/m$^3$ for pressure and find the velocity? The pipe length is 10 ft and diameter is 1 ft.

Also, to find density of the gas the ideal gas equation was used, relating pressure and temperature. For this gas, the temperature was 298 K.

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    $\begingroup$ $\Delta P$ is the pressure drop across the pipe, so it'd be zero if you assume the pressure constant. You do however have $f$ which accounts for friction so actually there has to be a pressure drop. $\endgroup$ – idkfa Mar 27 '16 at 11:21
  • $\begingroup$ Is this question different from your other one? $\endgroup$ – hazzey Mar 27 '16 at 11:49
  • $\begingroup$ @hazzey yes but all the values have changed $\endgroup$ – user510 Mar 27 '16 at 13:25
  • $\begingroup$ @idkfa is there a way to calculate the change in pressure? $\endgroup$ – user510 Mar 27 '16 at 13:25
  • $\begingroup$ @user510 That's the beauty of analytical solutions. You don't have to reinvent the wheel when have other numerical values. Regarding the pressure drop I'd cautiously lean towards no with the given values, but I'll leave that to the experts in fluid dynamics. $\endgroup$ – idkfa Mar 27 '16 at 13:48
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@idfka is correct there needs to be some pressure drop to overcome the friction and flow. In practice though for gas through 10 feet of pipe the pressure drop will not be in the measurable range unless the pipe is undersized.

So to answer your question, you can't calculate the velocity with the inputs you have. Not sure what your objective is here but what you can do can assume some typical numbers.

To calculate pressure drop, you can assume a velocity of around 60-80 ft/sec for gas. This value will be different if you're expecting liquid, particles or if its corrosive.

To calculate velocity, you can assume a pressure drop of about 6 psi/100 ft.

As for using the ideal gas law, assuming you have the molecular weight, that should be fine as pressures are quite low. You can just use the inlet density in the equation you have as its not gonna change much along the pipe.

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You can't just arbitrarily plug in the density of the air into the formula and say it's a pressure. What did you learn about units? Are the units of density and pressure the same?

The volume of the pipe is irrelevant to calculating the flow velocity over a given length. You do need to know the pressure at the inlet and the pressure at the outlet of the pipe.

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The key is to understand that you're not inputting the Pressure but the change in pressure ($\Delta P $) which is the difference between the upstream pressure and the back pressure downstream at the exit.

Otherwise yet you can input the standard density and an appropriate friction factor $f $

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