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

29.31 m

Step-by-step explanation:

It is given that flow rate Q =6.0 ltrs/minute
`=(6)/(1000* 60)`
`m^3/sec`

Diameter =10 mm

So radius =
`(10)/(2)=5 mm=5* 10^(-3)m`

Area of duct
`A=\pi r^2=3.14*(5* 10^(-3))^2=7.854 * 10^(-5)m^2`

Average velocity
`v=(Q)/(A)=(10^(-4))/(7.854* 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=(64)/(1800)=0.0356`

So head loss ifs given by
`(fLv_(avg)^2)/(d* 2* g)=(0.0356* 100* 1.732^2)/(10* 10^(-3)* 2* 9.81)=29.39\ m`