Pipe Contraction Calculator

In fluid dynamics, when a fluid flows through a pipe that contracts (i.e., the cross-sectional area decreases), we can calculate various properties using the principles of continuity and Bernoulli’s equation.

Key formulas for pipe contraction:

1. Continuity Equation (for incompressible flow):

   

   Where:

   • A1​ and A2​ are the cross-sectional areas at points 1 and 2 (before and after the contraction),
   • v1​ and v2 are the velocities at points 1 and 2 (before and after the contraction).

2. Velocity Change Due to Contraction: If the flow rate (Q) is constant, the velocity increases as the area decreases. You can calculate the velocity at the contracted section (v2) as:

   

3. Bernoulli’s Equation (for pressure difference):

   

   Where:

   • P1​ and P2​ are the pressures at points 1 and 2,
   • ρ is the fluid density,
   • v1​ and v2​ are the fluid velocities at points 1 and 2.

Steps for Calculation:

To calculate the velocity change, pressure change, or other properties, you'll need the following:

1. The diameter (or cross-sectional area) at both sections before and after the contraction.
2. The velocity or flow rate at the first section.
3. The fluid properties (e.g., density) if you want to calculate the pressure change.

Example of Pipe Contraction Calculation:

• Given:

  • Initial diameter D1=0.1 m,
  • Final diameter D2=0.05 m,
  • Initial velocity v1=2 m/s.

• Calculate:

  • The velocity at the contracted section using the continuity equation: