Question

What volume of the water per second can flow through a pipe 5.02 cm in diameter before turbulent flow will occur?

Assume that density of the water is 1000 kg/m3 and viscosity of the water 0.972 mPas.

Give your answer to two decimal places and you don't have to add unit cm3/s after your numerical value.

Answer 1

Given : D = 5.02 cm (0.0502 m) , $\rho$ = 1000 kg/m³ ; $\mu$ = 0.972×10^-3 Pas

Solution :

For a flow in a pipe of diameter D , experimental observations show that turbulent flow occurs when Reynolds number (R_e)>2000

Before turbulent flow occurs , we have

R_e = 2000

pud = 2000

2000(11) pd

2000 (0.972 10) (1000) (0.0502)

= 0.0387 m/s

Now volume per unit second is given by :

Q = A×v

= ($\pi$/4)(0.0502)²(0.0387)

= 76.65 cm³ /s