Question

Water at 98 F flows in a pipe 4 inches in diamter and 870 feet in length at a rate of 260 gallons per minute (GPM). What is the Reynolds number?

Answer 1

Answer:

Reynolds number is 293068.43.

Explanation:

Step1

Given:

Water temperature is 98 °F.

Diameter of the pipe is 4 in

Length of the pipe is 870 feet.

Flow rate of water is 260 gallons per minute.

Calculation:

Step2

Water kinematic viscosity at temperature 98 F is $7.55\times10^{-6}$ ft²/s.

Find the velocity of the water as follows:

Q=AV

$Q=\frac{\pi}{4}D^{2}V$

$(260 gal/min)(\frac{0.00222801 ft^{3}/s}{1 gal/min})=\frac{\pi}{4}(\frac{4}{12})^{2}V$

V=6.638 ft/s

Step3

Expression for Reynolds number is given as follows:

$Re=\frac{vd}{\nu}$

Here, v is velocity, $\nu$ is kinematic viscosity, d is diameter and Re is Reynolds number.

Substitute the values in the above equation as follows:

$Re=\frac{vd}{\nu}$

$Re=\frac{6.638\times(4in)(\frac{1ft}{12in})}{7.55\times10^{-6}}$

Re= 293068.43

Thus, the Reynolds number is 293068.43.