Hydraulic Machines MCQ with answer and solution

Concept

Specific speed is a characteristic constant for a series of geometrically similar pumps, used to classify pump types based on their performance and shape.

Formula

Ns = (N × √Q) / (g × H)^3/4

Step-by-step solution

1. Identify the formula for dimensionless specific speed: Ns = (N × √Q) / (g × H)^3/4. 2. Substitute the dimensions of each variable: N (Speed) = [T⁻¹], Q (Discharge) = [L³T⁻¹], g (Acceleration) = [LT⁻²], H (Head) = [L]. 3. Calculate the numerator dimensions: [T⁻¹] × [L³T⁻¹]^1/2 = [L^3/2 T^-3/2]. 4. Calculate the denominator dimensions: ([LT⁻²] × [L])^3/4 = [L²T⁻²]^3/4 = [L^3/2 T^-3/2]. 5. Divide numerator by denominator: [L^3/2 T^-3/2] / [L^3/2 T^-3/2] = [M⁰L⁰T⁰]. 6. Therefore, the dimension is dimensionless.

Explanation

In the context of dimensional analysis and similitude, the specific speed is derived as a dimensionless parameter (shape factor) to compare different types of pumps. While the practical specific speed used in engineering (Ns = N√Q / H³/⁴) has units depending on the system used, the fundamental 'dimensionless specific speed' (also known as the shape factor) is truly dimensionless when gravity (g) is included in the head term.

Why the other options are wrong

B: This is the unit for discharge (Q). C: This is the unit for velocity (v). D: This is the unit for angular velocity (ω).