Chemical Engineering - Fluid Mechanics - Discussion

Answer B is correct.

Darcy-Weisbach equation, Hf=4fl(V^2)/(2gd) shows that Hf is directly proportional to velocity^2 and f for Turbulent Flow=0.079/Re: Here Re=pvd/μ.

As f is a dimensionless number (Even V term comes in Co-efficient of friction formula), Hf 4flV^2 is correct. We can also refer Dimensional and Model Analysis.

Option A is wrong (Hf is not various with V).
Option B is Correct (Hf is various with V^2).
Option C is Wrong(Hf is not inversely as the square of diameter).
Option D is Wrong (Hf is not inversely as the velocity).

Here, hf​ = fD ​L​v2​/Dg.

Where hf​ is the head loss,
fD​ is the Darcy friction factor,
L is the pipe length,
D is the pipe diameter,
v is the average flow velocity,
And g is the gravitational acceleration.

h=4flv^2 / 2gd
for turbulent flow
f=0.079/Re^0.25
re=dvp/u
h directly propotional to v^1.75
nearly equal to 2
ans [B]

Darcy Weisbach equation use.

Ap = 4flV^2/2D.

Head loss is V^2/2g.

Pressure drop in a circular pipe in turbulent flow is proportional to velocity raised to the power of 1.7-1.9.

h = (4*f*(l/d)*v^2/2).

Friction factor (f) = (g*D*Head loss) / 2*v^2*L.

This is general equation shows head loss is directly proportional to velocity ^2.

Because head loss is:

HL = (F)X(L/D)X(V2/2g).

Where,

HL = Total Head Loss.

F = Friction factor related to the roughness inside the pipe.

L = Length of the pipe.

D = Diameter of the pipe.

V = Average liquid velocity in the pipe.

2g = Two times the Universal Gravitation Constant (g=32.2 ft/sec).

Anyone, Please explain this clearly.