Chemical Engineering - Fluid Mechanics - Discussion

Head loss is V^2/2g.

Darcy Weisbach equation use.

Ap = 4flV^2/2D.

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).

One part of erg equation, which is Burke Plummer equation for turbulent gives the relation of head loss is firstly proportional to velocity squared and inversely proportional to diameter.

Anyone, Please explain this clearly.

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).

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

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

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

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

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]