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

Reynolds number is 293068.43.

Step-by-step 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*10^(-6)` ft²/s.

Find the velocity of the water as follows:

Q=AV

`Q=(\pi)/(4)D^(2)V`

`(260 gal/min)((0.00222801 ft^(3)/s)/(1 gal/min))=(\pi)/(4)((4)/(12))^(2)V`

V=6.638 ft/s

Step3

Expression for Reynolds number is given as follows:

`Re=(vd)/(\\u)`

Here, v is velocity,
`\\u` is kinematic viscosity, d is diameter and Re is Reynolds number.

Substitute the values in the above equation as follows:

`Re=(vd)/(\\u)`

`Re=(6.638*(4in)((1ft)/(12in)))/(7.55*10^(-6))`

Re= 293068.43

Thus, the Reynolds number is 293068.43.