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Assuming that the thrust T of a propeller depends on the diameter D, speed of advance V, angular velocity ω, dynamic viscosity μ and mass density ρ, which of the following ’non -dimensional parameters can be derived ‘by dimensional analysis?
  • a)
    1,2 and 3
  • b)
    2, 3 and 4
  • c)
    1,3 and 4
  • d)
    1,2 and 4
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Assuming that the thrust T ofa propeller depends on the diameter D, sp...
Number of variables = 6
Number of dimensions = 3
Dimensionless parameters = 6 - 3 = 3.
Take D, V, and ρ as repeating variables.
VD/μ will not be dimensionless- number as its dimension is [M-1L3].
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Most Upvoted Answer
Assuming that the thrust T ofa propeller depends on the diameter D, sp...
Ω, and the density of the fluid ρ, we can write the equation for thrust as:

T = f(D, V, ω, ρ)

To determine the relationship between thrust and each of the variables, we need to consider the physical principles involved.

1. Diameter (D): The thrust generated by a propeller is directly proportional to the square of its diameter. This can be expressed as:

T ∝ D^2

2. Speed of advance (V): The thrust generated by a propeller is directly proportional to the cube of the speed of advance. This can be expressed as:

T ∝ V^3

3. Angular velocity (ω): The thrust generated by a propeller is directly proportional to the square of the angular velocity. This can be expressed as:

T ∝ ω^2

4. Density of the fluid (ρ): The thrust generated by a propeller is directly proportional to the density of the fluid. This can be expressed as:

T ∝ ρ

Combining these relationships, we can write the equation for thrust as:

T = k * D^2 * V^3 * ω^2 * ρ

where k is a constant that takes into account other factors such as efficiency, blade shape, and propeller design.
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Assuming that the thrust T ofa propeller depends on the diameter D, speed of advance V, angular velocity ω, dynamic viscosity μ and mass density ρ, which of the following ’non -dimensional parameters can be derived ‘by dimensional analysis?a)1,2 and 3b)2, 3 and 4c)1,3 and 4d)1,2 and 4Correct answer is option 'C'. Can you explain this answer?
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