Work Done By Pump Per Stroke Against Friction Calculator

Formula Used:

\[ W = \frac{2}{3} \times L \times \left( \frac{4 \times f \times L_{\text{pipe}}}{2 \times d_{\text{pipe}} \times g} \right) \times \left( \frac{A}{a_d} \times (\omega \times r) \right)^2 \]

Length of Stroke (L):

Friction Factor (f):

Length of Pipe (L_pipe):

Pipe Diameter (d_pipe):

Acceleration Due to Gravity (g):

m/s²

Area of Cylinder (A):

m²

Area of Delivery Pipe (a_d):

m²

Angular Velocity (ω):

rad/s

Crank Radius (r):

Work Done (W):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Work Done By Pump Per Stroke Against Friction Formula?

The Work Done By Pump Per Stroke Against Friction formula calculates the energy expended by a pump to overcome frictional forces during each stroke. This is essential for understanding pump efficiency and energy requirements in fluid systems.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ W = \frac{2}{3} \times L \times \left( \frac{4 \times f \times L_{\text{pipe}}}{2 \times d_{\text{pipe}} \times g} \right) \times \left( \frac{A}{a_d} \times (\omega \times r) \right)^2 \]

Where:

\( W \) — Work done (J)
\( L \) — Length of stroke (m)
\( f \) — Friction factor
\( L_{\text{pipe}} \) — Length of pipe (m)
\( d_{\text{pipe}} \) — Pipe diameter (m)
\( g \) — Acceleration due to gravity (m/s²)
\( A \) — Area of cylinder (m²)
\( a_d \) — Area of delivery pipe (m²)
\( \omega \) — Angular velocity (rad/s)
\( r \) — Crank radius (m)

Explanation: The formula accounts for the mechanical work required to overcome frictional losses in the pumping system, incorporating geometric and dynamic parameters of the pump and piping system.

3. Importance of Work Calculation

Details: Accurate work calculation is crucial for pump system design, energy efficiency analysis, and determining the power requirements for pumping operations. It helps in optimizing system performance and reducing operational costs.

4. Using the Calculator

Tips: Enter all values in appropriate units. Ensure all inputs are positive values. The calculator will compute the work done per stroke against friction in joules.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the friction factor in this calculation?
A: The friction factor represents the resistance to flow in the pipe system. Higher friction factors indicate greater energy losses due to pipe roughness and flow characteristics.

Q2: How does pipe length affect the work done?
A: Longer pipes generally result in higher frictional losses, requiring more work to overcome these losses during pumping operations.

Q3: Why is the area ratio (A/a_d) important?
A: The area ratio affects the flow velocity and pressure characteristics in the system, which directly influences the frictional losses and work required.

Q4: What are typical values for angular velocity in pumping systems?
A: Angular velocity varies by pump type and application, but typically ranges from 1-10 rad/s for many industrial pumping systems.

Q5: How accurate is this formula for real-world applications?
A: While the formula provides a good theoretical estimate, real-world systems may require additional factors to account for other losses, fittings, and system complexities.