SHORT QUESTION ANSWERS-FLOW MEASUREMENT       Flow measuring meters       Q. ANS. Weirs and Notches       FM introduction-1

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Question answers make a topic very

clear. It increases the depth of

understanding. The fundamentals

are applied easily in real life applications.

  1. Define circulation. How is it different from vorticity?


Circulation is defined as line integral of the tangential velocity about a closed path (contour). It is a scalar quantity. Its symbol is ɼ.


It is the tendency of a fluid particle to rotate or spin at a particular point. Vorticity is a vector quantity and is a mathematical measurement of local rotation or spin of the fluid. Thus, vorticity is microscopic measure of rotation at a point in a fluid. It depends on position and time. Vorticity is the curl of velocity vector. If the vorticity is zero, flow is ir-rotational. Its symbol is ’Ω’. It is defined as circulation per unit enclosed area

Ω = dɼ / A= dɼ / Δx. Δy = ∂v/∂x — ∂u/∂y

If vorticity exits, flow is rotational. If vorticity is zero, flow is ir-rotational.

Vorticity is two times the rotation. Ω=2 ω


Rotation (ω) = (1/2) (∂v/∂x — ∂u/∂y)

Thus vorticity, circulation and rotation occur in a viscous fluid.

  1. Which is the most accurate among Venturimeter, Orifice meter and rotameter? Write coefficient of discharge for each.

Venturimeter, Cd = 0.95 to 0.98

Rota meter, Cd = 0.70

Orifice, Cd = 0.62 to 0.65

The smaller the discharge coefficient, the larger the frictional head loss of the meter

Therefore most accurate is Venturimeter.

  1. Write the continuity equation in differential form.

  • For a compressible fluid

∂ (ρu)/ ∂x + ∂ (ρv)/ ∂y + ∂ (ρz)/ ∂z =0

  • For a in-compressible fluid

∂ (u)/ ∂x + ∂ (v)/ ∂y + ∂ (z)/ ∂z =0

  1. What is reason for the capillary action?

Adhesion and Cohesion are responsible for the capillary action. 

  1. What is the significance of lower and upper critical Reynolds number?

Reynolds critical numbers represents the type of flow. There are lower and upper Reynolds critical numbers. Lower critical number represents where the laminar flow ends.  Upper critical number represents where the turbulent flow starts. Flow between Reynolds lower and upper critical numbers represents transition flow.

  1. What is the basic principle used in the measurement of discharge in Venturimeter and Orifice meter?

 Bernoulli’s Theorem in which one form of head changes into another form of head. Pressure head changes into kinetic head. Difference of pressure head is used in the measurement of discharge in the Venturimeter and Orifice meter.

  1. Explain friction coefficient in laminar and turbulent flow in a pipe.

In general friction coefficient depends on (Re, k/D, area of cross section of the pipe)

Where k is the pipe roughness

 The Fanning’s friction coefficient, Cf, for a flow through a closed duct,

Cf = shear stress/(1/2) ρv2 in terms of wall shear stress

Darcy’s friction factor is defined as f = 4Cf (4 times Fanning friction coefficient)

Commonly used values of friction coefficient

f for a laminar flow in a pipe (from Darcy equation)

When Re number is known

f=64/Re for laminar flow in a pipe

  For a turbulent flow in a pipe,

f is found from Cole-brook equation

1/f1/2 =– 2 log [2.51/ (Re f1/2) + (k/dh)/3.72]

In this equation f occurs on both sides. f is found by iteration.

K =pipe roughness

dh = Hydraulic diameter used for non circular pipes = 4A/wetted perimeter of pipe