analytic solution for flow in tube

jeremy.rutman · May 26, 2020, 16:34

I have a pretty simple problem - air is forced into a tube of inner radius r at ground level, at speed V and pressure p1. The tube has an outlet at height h.

From bernoulli I have

$p1+1/2 \rho v_1^{2}=p2+1/2 \rho v_2^{2}+ \rho gh$

Let's say I know the air density at the inlet ,e.g. 1kg/m^3; can I determine the velocity,pressure, and density at the outlet ? It seems I need two more equations . I guess that in steady state there isnt any mass building up so that gives me

$\rho v_1^{2}= \rho v_2^{2}$

which leaves me one equation shy , is there another I'm not thinking of?

LuckyTran · May 27, 2020, 08:31

You need an equation of state for density.

agd · May 27, 2020, 08:35

You also don't have a continuity equation in your list. What you have is essentially energy and momentum.

May 26, 2020, 16:34	analytic solution for flow in tube	#1
jeremy.rutman New Member jeremy rutman Join Date: May 2020 Posts: 1 Rep Power: 0	I have a pretty simple problem - air is forced into a tube of inner radius r at ground level, at speed V and pressure p1. The tube has an outlet at height h. From bernoulli I have $p1+1/2 \rho v_1^{2}=p2+1/2 \rho v_2^{2}+ \rho gh$ Let's say I know the air density at the inlet ,e.g. 1kg/m^3; can I determine the velocity,pressure, and density at the outlet ? It seems I need two more equations . I guess that in steady state there isnt any mass building up so that gives me $\rho v_1^{2}= \rho v_2^{2}$ which leaves me one equation shy , is there another I'm not thinking of?

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May 27, 2020, 08:31		#2
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,674 Rep Power: 66	You need an equation of state for density.

May 27, 2020, 08:35		#3
agd Senior Member Join Date: Jul 2009 Posts: 353 Rep Power: 18	You also don't have a continuity equation in your list. What you have is essentially energy and momentum.