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

Answer:

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

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 $\nu =1.24\times 10^{-6}$ 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:  

$A_{1}V_{1}=A_{2}V_{2}$  

$\frac{\pi}{4}d^{2}_{1}V_{1}=\frac{\pi}{4}d^{2}_{2}V_{2}$  

Substitute the values in the above equation as follows:  

$\frac{\pi}{4}2^{2}\times 3=\frac{\pi}{4}3^{2}V_{2}$  

$2^{2}\times 3=3^{2}V_{2}$  

$V_{2}=\frac{4}{3}$ m/s.  

Step2

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

$Re=\frac{v_{1}d_{1}}{\nu }$  

$Re=\frac{2\times 3}{1.24\times 10^{-6}}$  

Re=4838709.677  

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

$Re=\frac{v_{2}d_{2}}{\nu }$  

$Re=\frac{\frac{4}{3}\times 3}{1.24\times 10^{-6}}$  

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.