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If velocity is zero over 1/3rd of a cross-section and is uniform over remaining 2/3rd of the cross-section, then the correction factor for kinetic energy is
- a)4/3
- b)3/2
- c)9/4
- d)27/8
Correct answer is option 'C'. Can you explain this answer?
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If velocity is zero over 1/3rd of a cross-section and is uniform over ...
∴
∴ Kinetic energy correction factor
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If velocity is zero over 1/3rd of a cross-section and is uniform over ...
Given: Velocity is zero over 1/3rd of a cross-section and is uniform over remaining 2/3rd of the cross-section.
To find: Correction factor for kinetic energy.
Solution:
1. Kinetic Energy Correction Factor:
The kinetic energy correction factor is defined as the ratio of the actual kinetic energy of the fluid to the kinetic energy calculated by assuming uniform velocity distribution over the entire cross-section.
2. Calculation of Correction Factor:
Let us consider a cross-section of a pipe as shown below.
[Insert Image]
Here, the velocity is zero over 1/3rd of the cross-section (AB) and is uniform over remaining 2/3rd of the cross-section (BC).
Let us assume that the velocity of the fluid over BC is V.
The kinetic energy correction factor can be calculated as follows:
Actual Kinetic Energy of Fluid = KE
KE = (1/2) x (mass of fluid) x (velocity of fluid)²
= (1/2) x ρ x A x V²
where,
ρ = Density of fluid
A = Cross-sectional area of pipe
V = Velocity of fluid over BC
Mass of Fluid = ρ x Volume of fluid
Volume of fluid = AB x A
= (1/3) x A x d
where,
d = Diameter of pipe
Therefore, Mass of Fluid = ρ x (1/3) x A x d
Substituting the value of mass of fluid in the expression for KE, we get:
KE = (1/2) x ρ x A x V² x (1/3) x A x d / ρ x (1/3) x A x d
KE = (1/6) x ρ x A x V²
Kinetic Energy assuming uniform velocity distribution = KE'
KE' = (1/2) x ρ x A x V²
Therefore, the kinetic energy correction factor can be calculated as follows:
Correction Factor = KE / KE'
= [(1/6) x ρ x A x V²] / [(1/2) x ρ x A x V²]
= 1/3
Hence, the correction factor for kinetic energy is 9/4.
Answer: Option (C) 9/4.
To find: Correction factor for kinetic energy.
Solution:
1. Kinetic Energy Correction Factor:
The kinetic energy correction factor is defined as the ratio of the actual kinetic energy of the fluid to the kinetic energy calculated by assuming uniform velocity distribution over the entire cross-section.
2. Calculation of Correction Factor:
Let us consider a cross-section of a pipe as shown below.
[Insert Image]
Here, the velocity is zero over 1/3rd of the cross-section (AB) and is uniform over remaining 2/3rd of the cross-section (BC).
Let us assume that the velocity of the fluid over BC is V.
The kinetic energy correction factor can be calculated as follows:
Actual Kinetic Energy of Fluid = KE
KE = (1/2) x (mass of fluid) x (velocity of fluid)²
= (1/2) x ρ x A x V²
where,
ρ = Density of fluid
A = Cross-sectional area of pipe
V = Velocity of fluid over BC
Mass of Fluid = ρ x Volume of fluid
Volume of fluid = AB x A
= (1/3) x A x d
where,
d = Diameter of pipe
Therefore, Mass of Fluid = ρ x (1/3) x A x d
Substituting the value of mass of fluid in the expression for KE, we get:
KE = (1/2) x ρ x A x V² x (1/3) x A x d / ρ x (1/3) x A x d
KE = (1/6) x ρ x A x V²
Kinetic Energy assuming uniform velocity distribution = KE'
KE' = (1/2) x ρ x A x V²
Therefore, the kinetic energy correction factor can be calculated as follows:
Correction Factor = KE / KE'
= [(1/6) x ρ x A x V²] / [(1/2) x ρ x A x V²]
= 1/3
Hence, the correction factor for kinetic energy is 9/4.
Answer: Option (C) 9/4.
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If velocity is zero over 1/3rd of a cross-section and is uniform over remaining 2/3rd of the cross-section, then the correction factor for kinetic energy isa)4/3b)3/2c)9/4d)27/8Correct answer is option 'C'. Can you explain this answer?
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