Question

In a circular tube the diameter changes abruptly from D1 = 2 m to D2 = 3 m. The flow velocity in the part with smaller diameter is vi = 3 m/s. Determine if for water in the both parts of the tube there is laminar flow or tubulent flow. The kinematic viscosity of water is v= 1.24. 10^-6

Answer 1

The flow is turbulent at both the parts of the tube.

Step-by-step explanation:

Given:

Water is flowing in circular tube.

Inlet diameter is
`d_(1)= 2`m.

Outlet diameter is
`d_(2)= 3`m.

Inlet velocity is
`V_(1)= 3` m/s.

Kinematic viscosity is
`\\u =1.24*  10^(-6)` m²/s.

Concept:

Apply continuity equation to find the velocity at outlet.

Apply Reynolds number equation for flow condition.

Step1

Apply continuity equation for outlet velocity as follows:

`A_(1)V_(1)=A_(2)V_(2)`

`(\pi)/(4)d^(2)_(1)V_(1)=(\pi)/(4)d^(2)_(2)V_(2)`

Substitute the values in the above equation as follows:

`(\pi)/(4)2^(2)* 3=(\pi)/(4)3^(2)V_(2)`

`2^(2)* 3=3^(2)V_(2)`

`V_(2)=(4)/(3)` m/s.

Step2

Apply Reynolds number formula for the flow condition at inlet as follows:

`Re=(v_(1)d_(1))/(\\u )`

`Re=(2* 3)/(1.24*  10^(-6))`

Re=4838709.677

Apply Reynolds number formula for the flow condition at outlet as follows:

`Re=(v_(2)d_(2))/(\\u )`

`Re=((4)/(3)* 3)/(1.24* 10^(-6))`

Re=3225806.452

Thus, the Reynolds number is greater than 2000. Hence the flow is turbulent.

Hence, the flow is turbulent at both the parts of the tube.