Question

Water from a pipe is coming at a rate of 100 liters per minute. If the radius of the pipe is 5 cm, the Reynolds number for the flow is of the order of ______.

(density of water = 1000 kg/m³, coefficient of viscosity of water = 1 mPa s)

Options

• 10³

• 10⁴

• 10²

• 10⁶

Answer 1

Water from a pipe is coming at a rate of 100 liters per minute. If the radius of the pipe is 5 cm, the Reynolds number for the flow is of the order of 10^4.

Explanation:

Given: The pipe's radius is r = 5 cm, and the rate of flow of water coming out of the pipe is

`V/t = 100 "litres"/"minute" = 100/60 "litres"/"second"`,

the density of water is ρ = `1000 "kg"/"m"^3`,

The water viscosity coefficient is η = 1 mPa s.

To find: The order of magnitude of the flow's Reynolds number.

The Reynolds number for liquid flow is:

`R_e = (rhovD)/η`

(`v = (V/t)/A` is the velocity of flow, A is an area of cross A section of pipe and D = 2r is the diameter of the pipe.)

`R_e = (2rhoVr)/(tAη)`

= `(2rhoVr)/(tpir^2η)`

= `(2rhoV)/(rpitη)`

= `(2 xx 1000 xx 100 xx 10^-3)/(0.05 xx 3.14 xx 60 xx 1 xx 10^-3) = 2 xx 10^4`