SHORT QUESTION ANSWERS-FLUID MECHANICS       Fluid properties & forces       Cavitation       Drag       Hydro Forces on Surfaces       Q. ANS. Viscosity       Bernoulli’s Energy Momentum equations       Pressure measurement        Q. ANS. Fluid Mechanics          Q. ANS. Hydro Boundary Layer





Question answers improve clarity.

It gives a deep understanding.

Corrective measures are taken to

reduce the pressure drop.

1. What is difference between Darcy and Fanning equations for the pressure drop in a fluid flow?

Darcy friction factor is four times the Fanning friction factor. Darcy friction factor is also called as Moody friction factor or Blasius friction factor.

  •  laminar flow, Darcy friction factor = fD= 64/Re

Where Re is Reynolds number

  •  turbulent flow,

Darcy friction factor = fD= 0.06 to 0.006

Fanning friction factor (ff) is one fourth of Darcy friction factor.

For a laminar flow

ff = 16/Re = ζ /ρu2/2


ff is the local Fanning friction factor

ζ is the local shear stress

u is the local flow velocity

ρ is the density of the fluid

Δhff = 2ff u2L/gD

For turbulent flow, Colebrook equation is used to find Fanning friction factor

1/ ( ff)0.5 = -4.0 log10 ((ε/d) / 3.7 + 1.256/ ff)

Where ε, roughness of the inner surface of the pipe (dimension of length);

     d, inner pipe diameter;

ff appears on both sides of the equation and its solution can be found only by hit and trial.

Darcy–Welsbach factor, fD is more commonly used by civil and mechanical engineers, and the Fanning factor, f, by chemical engineers, but one must be careful to determine correctly the friction factor for the equation used. Fanning equation is used by chemical engineers.

  1. State the assumptions used in the Bernoulli’s theorem.

Assumptions used in the derivation of Bernoulli’s theorem are

  • Fluid is ideal i.e. there are no losses of any kind in the flow of an ideal fluid.

  • Flow is steady i.e. No changes in the flow velocity with respect to time.

  • Fluid is incompressible i.e. It is only for liquids i.e. although pressure changes are there but volume and hence density remains constant during the flow.

  • Flow is one dimensional.

  • Fluid is continuous i.e. there are no vapors in it or there are no impurities in it.

  • Only gravitational and pressure forces are acting on the fluid i.e. fluid is non viscous.

2. State Pascal’s Law.

Pressure at any point in a static fluid is same in all the directions. If there is an increase/decrease in pressure at any point in a confined fluid, there is an equal increase/decrease of pressure at every other point in the container.

3. What is a Froude’s number? What is its significance?

Froude’s number (We) is a square root of the ratio of inertia force to the gravitational force. It is a dimensionless number. Mathematically

Fr = V/ (Dg)0.5

V is the velocity in m/s, assuming full pipe flow
D is the pipe inner diameter in m
g is the gravity constant in m/s²

Experimentally it has been found that Froude number should be less than 0.3 to avoid air entrainment and ensure undisturbed flow without pulsations.

The Froude number compares the resistance to wave making between bodies of various sizes and shapes. In free surface flow, it has been found that

  • When Froude Number = 1, flow is critical.

  • If Froude Number > 1, flow is super-critical.

  • When Froude Number < 1, flow is sub-critical.

In appearance, it has similarity with Mach number. Froude’s number is used in a fluid flow around marines, over spillways or flow over the weirs in open channels.