Pumps

Overview

Engineering reference data for Pumps in fluid mechanics.

Key Formulas

Reynolds Number

$Re = \frac{\rho v D}{\mu}$

Ratio of inertial to viscous forces — determines flow regime.

Bernoulli's Equation

$P + \frac{1}{2}\rho v^2 + \rho g h = \text{const}$

Conservation of energy for steady, inviscid, incompressible flow.

Continuity Equation

$A_1 v_1 = A_2 v_2$

Conservation of mass for incompressible flow.

Darcy-Weisbach

$\Delta P = f \frac{L}{D} \frac{\rho v^2}{2}$

Pressure drop due to friction in a pipe.

Variables

Pump Classifications

Pumps are broadly classified into two main types based on their operating principles:

1. Centrifugal Pumps: Use a rotating impeller to impart kinetic energy to the fluid, which is then converted to pressure energy in the casing. They are suitable for high flow rates and low-to-medium pressure applications.
2. Positive Displacement Pumps: Move fluid by trapping a fixed volume and forcing it into the discharge pipe. Examples include gear pumps, piston pumps, and screw pumps. They are suitable for high pressure and low flow rate applications.

Centrifugal Pump Details

Affinity Laws

The performance of a centrifugal pump changes predictably with variations in speed ($N$) or impeller diameter ($D$). The affinity laws are:

$$\frac{Q_1}{Q_2} = \frac{N_1}{N_2} = \frac{D_1}{D_2}$$ $$\frac{H_1}{H_2} = \left(\frac{N_1}{N_2}\right)^2 = \left(\frac{D_1}{D_2}\right)^2$$ $$\frac{P_1}{P_2} = \left(\frac{N_1}{N_2}\right)^3 = \left(\frac{D_1}{D_2}\right)^3$$

Where:

• $Q$ = Volume flow rate
• $H$ = Head
• $P$ = Power consumption

Specific Speed ($N_s$)

Specific speed is a dimensionless parameter used to characterize the impeller shape and performance of a centrifugal pump.

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

Suction Specific Speed ($N_{ss}$)

Used to evaluate a pump's susceptibility to cavitation and define its stable operating range.

$$N_{ss} = \frac{N \sqrt{Q}}{NPSH_r^{3/4}}$$

Where $NPSH_r$ is the net positive suction head required.

Key Concepts

Net Positive Suction Head (NPSH)

• NPSH Available ($NPSH_a$): The absolute pressure at the pump suction minus the fluid's vapor pressure. It is a property of the system.
• NPSH Required ($NPSH_r$): The minimum pressure required at the pump suction to avoid cavitation. It is a property of the pump. To avoid cavitation: $NPSH_a > NPSH_r$

Cavitation

Cavitation occurs when the local static pressure in a fluid falls below its vapor pressure, causing vapor bubbles to form. These bubbles collapse violently when they move into a region of higher pressure, causing noise, vibration, and severe erosion of the impeller.

Best Efficiency Point (BEP)

The operating point (flow rate) on a pump's performance curve where efficiency is maximized. Operating near BEP minimizes energy use and maximizes pump longevity.

Pump Power Calculation

The hydraulic power ($P_h$) required by the pump is:

$$P_h = \rho g Q H$$

Where:

• $\rho$ = fluid density
• $g$ = acceleration due to gravity
• $Q$ = volume flow rate
• $H$ = total developed head

The shaft power ($P_s$) is the power supplied to the pump shaft and is greater than the hydraulic power due to efficiency losses:

$$P_s = \frac{P_h}{\eta}$$

Where $\eta$ is the overall pump efficiency.

System Curve vs. Pump Performance Curve

The intersection of the system curve (which shows the head loss in a piping system as a function of flow rate) and the pump performance curve (which shows the head produced by the pump as a function of flow rate) defines the operating point of the pump in the system.

Interactive Charts

References

• Original Source