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.

Why so confusing. It's simply asking head loss and is directly proportional to the square of the velocity that's it.

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

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

Laminar directly proportional to velocity (hagen poisellea eqn} and in case turbulent proportional to square of velocity (darcy formula).

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.