Question

an ideal gas is flowing in a constant diameter pipe at a constant temprature. what is the relation of average velocity to pressure

Answer 1

Answer:

V = mRT /  ($\frac{\pi }{4}$d²)PM

Therefore, pressure decreases as velocity increases.

This is a hypothetical concept as the friction which causes the velocity to increases also makes the pressure decrease.

Explanation:

Given the data in the question;

we know that an ideal gas equation is;

$_p$ = PM/RT --------------- let this be equation 1

P is pressure, M is molecular weight, R is universal gas constant and T is the absolute temperature.

The volumetric flow rate from the continuity equation is;

Q = AV

and A =  $\frac{\pi }{4}$d²

so, Q = ($\frac{\pi }{4}$d²)V ---------let this be equation 2

Expression for mass m in flowrate is;

m = Q$_p$ ------------------let this be equation 3

so, m = ($\frac{\pi }{4}$d²)V × PM/RT

solve for V

V = mRT /  ($\frac{\pi }{4}$d²)PM

Therefore, pressure decreases as velocity increases.

This is a hypothetical concept as the friction which causes the velocity to increases also makes the pressure decrease.