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GATE CE 2021 Official Paper: Shift 2

Option 1 : 2/3

CT 1: Engineering Mathematics

1084

10 Questions
10 Marks
12 Mins

__Explanation__:

a) Momentum correction factor (β):

The momentum correction factor is defined as the ratio of momentum of the flow per second based on actual velocity to the momentum of the flow per second based on average velocity across a section.

\(β = \;\frac{{Momentum\;per\;second\;based\;on\;actual\;velocity}}{{Momentum\;per\;second\;based\;on\;average\;velocity}}\)

⇒ \(β = \frac{1}{{A{V^2}}}\smallint {u^2}.dA\)

For turbulent flow, the momentum correction factor is slightly higher than one near to 1.2 and

for laminar, its value is 1.33 = 4/3 --- (1)

b) Kinetic energy correction factor(α):

- It is defined as the ratio of
*kinetic energy/second based on actual velocity to the kinetic energy/second based on average velocity.* - \(α = \frac{1}{A}\mathop \smallint \limits_A^{} {\left( {\frac{u}{V}} \right)^3}dA\)
- where A = area, V= average velocity, u= local velocity at distance r.
- For laminar flow in a circular pipe α = 2 --- (2)

(1) divided by (2)

∴ Ratio of β/α = (4/3)/2 = 2/3