Mechanical Engineering - Hydraulics and Fluid Mechanics - Discussion

Here is solution to the contradictions, please read this carefully.

Head loss due to viscosity in case of laminar flow in pipe = 32μvl/wd^2

In this question, Head loss due to friction in pipe = 4flv^2/2gd will not be considered because this equation holds for head loss due to friction in the pipe(for both, laminar and turbulent), not for head loss due to 'viscosity in case of laminar flow' in pipe.

Since, for laminar flow condition viscosity is dominant over inertia of fluid flowing, hence head loss due to viscosity is being considered and i.e. 32μvl/wd^2.

In fact, head loss due to friction will also act in case of laminar flow but in this question head loss due to laminar flow(i.e. head loss due to viscosity) is being asked only.
So, in this question, Head loss is proportional to Velocity.

The question is about the loss of PRESSURE HEAD, not HEADLOSS (Hf).

So the correct answer is PRESSURE HEAD = 32μvl/wd^2.

Actually Hf= 4flVsq/2gd.

But friction factor 4f = 64/Re.
And Re = RoVD/Mu.
Thus Vsq and V cancel each other gives V on vthe numerator. Hence Hf is proportional to V.

I think answer is (velocity)2.
As change(pressure) = row*g*h.

h=flv2/2gd.
So change(pressure) directly proportional to v2.

Answer is right.

Loss of head = [32u*V(average)L]/r*g*d^2.

V(Average) = Average velocity.

For Laminar flow :

Loss of head = hF = [32*u*V(average)L]/r*g*d^2.

For turbulent flow:

HF = (flv^2)/(2*g*d).

In q they called loss of pressure head not friction head loss. So I think answer is right.

4flv2/2gd is a loss of pressure head and velocity is taken.

Whereas 32vl/d2 is a pressure drop and here average velocity is calculated.

Hence the answer given is contradictory.

Re is directly proportion to v.
f = 16/Re.
Hf = 4flv^2/2gd.
So, Hf is proportion to v.

Right answer because in pipe flow laminar 32u*v (average velocity) L/roh*g*d2.