Question

If \(\eta_z =\) specific speed, \(\eta_1 =\) pump speed, \(Q =\) pump discharge, \(H =\) total head, then the mathematical expression for specific speed of a pump is:

• A. \(\eta_z = \eta_1 \frac{\sqrt{Q}}{H^{3/4}}\)
• B. \(\eta_z = \eta_1 \frac{Q^{1/2}}{H^{3/4}}\)
• C. \(\eta_z = \eta_1 \frac{\sqrt{Q}}{H}\)
• D. \(\eta_z = \eta_1 \frac{Q^{1/2}}{H^{3/2}}\)

Hint:

Specific speed formula: \(\eta_z = \eta_1 \frac{Q^{1/2}}{H^{3/4}}\).
Used for pump classification:
- Low specific speed: Radial flow pumps (centrifugal).
- Medium specific speed: Mixed flow pumps.
- High specific speed: Axial flow pumps (propeller).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Specific speed of a pump is a dimensionless parameter used to classify pumps.

Step 2: Key Formula or Approach:
The formula for specific speed of a pump is:
\[ \eta_z = \eta_1 \frac{Q^{1/2}}{H^{3/4}} \] where:
- \(\eta_z\) = Specific speed
- \(\eta_1\) = Pump speed (rpm)
- \(Q\) = Pump discharge (m³/s)
- \(H\) = Total head (m)

Step 3: Detailed Explanation:
The specific speed formula helps in selecting the type of pump for a given application.
Option A: \(\eta_z = \eta_1 \frac{\sqrt{Q}}{H^{3/4}}\) - same as B (since \(\sqrt{Q} = Q^{1/2}\)).
Option B: \(\eta_z = \eta_1 \frac{Q^{1/2}}{H^{3/4}}\) - correct formula.
Option C: \(\eta_z = \eta_1 \frac{\sqrt{Q}}{H}\) - incorrect (H should be \(H^{3/4}\)).
Option D: \(\eta_z = \eta_1 \frac{Q^{1/2}}{H^{3/2}}\) - incorrect exponent for H.
Thus, the correct expression is \(\eta_z = \eta_1 \frac{Q^{1/2}}{H^{3/4}}\).

Step 4: Final Answer:
Thus, the mathematical expression for specific speed is \(\eta_z = \eta_1 \frac{Q^{1/2}}{H^{3/4}}\).
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