The specific speed of a centrifugal pump is defined as the speed of geometrically similar pump which would -

Question

Prepp Team · Accepted Answer

Understanding the Specific Speed of a Centrifugal Pump

The specific speed ($\boldsymbol{N_s}$) is a characteristic parameter used to classify pump impellers based on their geometric shape and hydraulic performance. It is defined as the speed of a geometrically similar pump impeller which would deliver unit discharge at unit head.

Mathematically, the specific speed for a centrifugal pump is typically expressed by the formula:

$$N_s = \frac{N\sqrt{Q}}{H^{3/4}}$$

Where:

$N$ is the rotational speed of the pump impeller (usually in RPM).
$Q$ is the flow rate or discharge per eye for double-suction pumps (usually in US Gallons per minute (gpm) or m<sup>3</sup>/s).
$H$ is the head developed per stage (usually in feet or meters).

The specific speed value is independent of the size of the pump and is the same for all geometrically similar pumps operating at their point of maximum efficiency. It provides insight into the general shape of the impeller and the type of flow (radial, mixed, or axial) it is designed for.

Analyzing the Specific Speed Definition Options

The question asks for the definition of specific speed based on the performance of a geometrically similar pump under specific conditions. Let's examine the given options in light of the specific speed formula:

Deliver unit discharge at unit power: This option involves power. Power ($P$) is related to discharge ($Q$) and head ($H$) by $P \propto Q \cdot H$. Defining specific speed based on unit power and unit discharge would not directly result in $N_s = N$ when $Q=1$ and $H=1$.
Produce unit power with unit head: Similar to the first option, this involves power and head. It doesn't align with the standard definition based on unit discharge and unit head.
Deliver unit discharge at unit head: Let's consider this option in the specific speed formula. If we set the discharge $Q = 1$ (unit discharge) and the head $H = 1$ (unit head), the formula becomes:
$$N_s = \frac{N\sqrt{1}}{1^{3/4}} = \frac{N \cdot 1}{1} = N$$

This shows that under the condition of delivering unit discharge at unit head, the specific speed ($\boldsymbol{N_s}$) is numerically equal to the speed ($N$) of that geometrically similar pump. This matches the conventional definition of specific speed.
Require unit power to develop unit head: This option again involves power, which is not the basis for the primary definition of specific speed in terms of flow rate and head.

Conclusion: Correct Definition of Specific Pump Speed

Based on the analysis of the specific speed formula and its standard definition, the specific speed of a centrifugal pump is indeed defined as the speed of a geometrically similar pump which would deliver unit discharge at unit head.

Revision Table: Key Pump Formulas

Parameter	Formula	Common Units (US Customary)	Common Units (SI)
Specific Speed ($N_s$) - Pump	$\frac{N\sqrt{Q}}{H^{3/4}}$	$N$: RPM, $Q$: gpm, $H$: ft	$N$: rev/s, $Q$: m<sup>3</sup>/s, $H$: m
Power ($P$) - Pump	$\frac{\rho g Q H}{\eta}$	$P$: hp, $Q$: gpm, $H$: ft, $\rho$: lb/ft<sup>3</sup> (with conversion)	$P$: Watts, $Q$: m<sup>3</s>, $H$: m, $\rho$: kg/m<sup>3</sup>

Additional Information: Specific Speed and Pump Types

The specific speed value helps categorize pumps and predict their characteristics. Different ranges of specific speed correspond to different impeller designs and are suitable for varying flow and head conditions.

Low Specific Speed ($N_s < 1500$ USCS or < 30 SI): These typically correspond to radial flow impellers (centrifugal pumps). They are best suited for high head and low flow rate applications. The impeller is narrow and of large diameter.
Medium Specific Speed ($1500 < N_s < 4000$ USCS or $30 < N_s < 80$ SI): These correspond to mixed-flow impellers, which have characteristics between radial and axial flow. They are used for medium head and medium flow rate applications.
High Specific Speed ($N_s > 4000$ USCS or > 80 SI): These correspond to axial flow impellers (propeller pumps). They are best suited for low head and high flow rate applications. The impeller resembles a propeller.

Understanding specific speed is crucial for selecting the appropriate pump type for a given application's head and flow requirements.