Test: Turbulent Flow in Pipes - Civil Engineering (CE) MCQ

In turbulent flow shear stress 
τ = τ₀ (1 - y/r₀) 
where,
r₀ = Radius of pipe
y = Distance measured from pipe wall
_ζ0 = Shear stress at boundary

Turbulent flow
For smooth pipe,

Average velocity,

g₀ = radius of pipe
y = distance measured from pipe boundary
u = shear velocity

from equation (i)

(iii) - (ii) gives
(b) Rough pipe

It gives,

same for both pipes rough or smooth

In turbulent flow shear stress at distance y from pipe boundary,

A fluid motion is said to be turbulent when the fluid particles move in an entirely haphazard or disorderly manner, that results in a rapid and continuous mixing of the fluid leading to momentum transfer as flow occurs. At any point in a turbulent flow the velocity and pressure are the functions of time thereby rendering such a flow as unsteady.

Explanation:

1. Smaller eddy size: Turbulent flow consists of swirling vortices or "eddies". The smaller the eddy, the higher the rate of energy dissipation. This is because smaller eddies have a higher surface area to volume ratio, leading to higher friction and thus more energy dissipation.

2. Lower viscosity: Viscosity is a measure of a fluid's resistance to shear or flow. Lower viscosity means less resistance to flow, allowing for more turbulence and thus more energy dissipation.

3. Large intensity of turbulence: The greater the turbulence, the more energy is dissipated. Turbulence involves the random and chaotic motion of fluid particles, which leads to a high rate of energy dissipation.

So, all these factors - smaller eddy size, lower viscosity, and large intensity of turbulence - would entail a greater energy dissipation in turbulent flow.

Reynolds number, R_e = Vd/v 
When R_e < R_ec Laminar flow occurs at very small velocities or through narrow passage (small d) or for highly viscous fluids (high v) the Re will be small and flow will remain laminar. For high velocities through large passage Reynolds number will be sufficient to cause turbulence.

k_s = 0.10 mm
τ = 7.85 N/m²

Since roughness value lies between 4 and 100 the pipe act as in transition.