Question

A fluid flows through a 10-mm diameter tube at a Reynolds number of 1800. If the flow rate is 6.0 liters/min, what is the head loss in 100 m length of tubing?

Answer 1

Answer:

29.31 m

Explanation:

It is given that flow rate Q =6.0 ltrs/minute $=\frac{6}{1000\times 60}$ $m^3/sec$

Diameter =10 mm

So radius =  $\frac{10}{2}=5 mm=5\times 10^{-3}m$

Area of duct $A=\pi r^2=3.14\times(5\times 10^{-3})^2=7.854 \times 10^{-5}m^2$

Average velocity $v=\frac{Q}{A}=\frac{10^{-4}}{7.854\times 10^{-5}}=1.372 m/sec$

The given Reynolds number is 1800 which is less than 2000 so it will be a laminar flow

So Reynolds number friction factor $f=\frac{64}{1800}=0.0356$

So head loss ifs given by $\frac{fLv_{avg}^2}{d\times 2\times g}=\frac{0.0356\times 100\times 1.732^2}{10\times 10^{-3}\times 2\times 9.81}=29.39\ m$