Respuesta :
Answer:
The mean velocity is 13 ft/s.
The Reynolds number is 88,583 and it is dimensionless.
Explanation:
We have water flowing in a pipe of 1.05 in diameter.
The density is Ļ=62.3 lb/ft and the viscosity is 1.2 cP.
The mean velocity can be calculated as
[tex]u=\frac{Q}{A}=\frac{Q}{\pi*D^2/4}=\frac{35gpm }{3.14*(1.05in)^2/4}\\\\ Ā u=\frac{35}{0.865}*\frac{gal}{min}\frac{1}{in^2}*\frac{231in^3}{1gal}*\frac{1}{60s} \\\\ Ā Ā u=156\,in/s=13\,ft/s[/tex]
The Reynolds number now can be calculated for this flow as
[tex]Re=\frac{\rho*u*D}{\mu}[/tex]
being Ļ: density, u: mean velocity of the fluid, D: internal diameter of the pipe and Ī¼ the dynamic viscosity.
To simplify the calculation, we can first make all the variables have coherent units.
Viscosity
[tex]\mu=1.2cP=\frac{1.2}{100}\frac{g}{cm*s}*\frac{1lb}{453.6g}*\frac{30.48cm}{1ft}= 0.0008\frac{lb}{ft*s}[/tex]
Diameter
[tex]D=1.05in*(\frac{1ft}{12in} )=0.0875ft[/tex]
Then the Reynolds number is
[tex]Re=\frac{\rho*u*D}{\mu}\\\\Re=62.3\frac{lb}{ft^3}*13\frac{ft}{s} *0.0875ft*\frac{1}{0.0008}*\frac{ft*s}{lb}\\\\Re=88,583[/tex]
