Calculating Air Velocity in a Pipe

[Karol]

Homework Statement

air flows in a 4" pipe. at point A a 2[bar] pressure was measured and the temperature was 22°C. the velocity V₁was 5[m/sec].
At point B, down the stream, a 1.2[bar] pressure was measured and the temperature was 32°C.
What is the velocity V₂at point B.

Homework Equations

The continuity equation:
\gamma₁A₁V₁=\gamma₂A₂V₂
Where \gamma=specific gravity, A=section area.

The gas law:
pv=RT
Where: p=absolute pressure
v=\frac{1}{\rho}, \rho=specific mass

The Attempt at a Solution

The specific gravity at point A:
\gamma_1=10\frac{2E5}{287\cdot 295}=23.6[N/m^3]

The specific gravity at point B:
\gamma_2=10\frac{1.2E5}{287\cdot 305}=13.7[N/m^3]


The continuity equation, without the area, since it's the same on both points:
23.6\cdot 5=13.7\cdot V_2 \Rightarrow V_2=8.6
The answer should be 7.05.

 

[TSny]

Are the measured pressures "gauge pressures"?

 

[Karol]

the problem statement is exactly as written in the book.
Maybe they should be, but that's the books mistake.

 

[TSny]

the problem statement is exactly as written in the book.
Maybe they should be, but that's the books mistake.

Well, measurements of pressure are often gauge pressures. See what you get for the answer if you assume they are gauge pressures

 

[Karol]

yes, thank you, it solved. bye