Force momentum principles applied to pipe flow.xls

Purpose of calculation: Use the force-momentum principle to calculate the forces applied to the fluid by the pipe in the x and y directions, Fx and Fy respectively.

Calculation Validation: Validated against worked example in lecture notes.

Calculation Reference

Hydraulics

Fluid Mechanics

The force-momentum principle, also known as Newton's second law of motion, states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. In fluid dynamics, this principle can be applied to calculate the forces acting on a fluid within a pipe.

Assuming steady-state incompressible flow and ignoring the effects of gravity, the forces applied to the fluid by the pipe can be calculated using the following equations:

Fx = m * ax = m * (V_out_x - V_in_x) / t Fy = m * ay = m * (V_out_y - V_in_y) / t

where:

• Fx and Fy are the forces applied to the fluid by the pipe in the x and y directions, respectively
• m is the mass of the fluid within the control volume
• ax and ay are the accelerations of the fluid in the x and y directions, respectively
• V_in_x and V_in_y are the x and y components of the fluid's velocity entering the pipe
• V_out_x and V_out_y are the x and y components of the fluid's velocity exiting the pipe
• t is the time interval over which the velocity changes occur

To use these equations to calculate Fx and Fy, you need to obtain the mass of the fluid (m) within the control volume and the fluid's velocities (V_in_x, V_in_y, V_out_x, and V_out_y) at the inlet and outlet of the pipe. The mass of the fluid can be calculated using the following equation:

m = ρ * V * A

where:

• ρ is the fluid density
• V is the average fluid velocity within the control volume
• A is the cross-sectional area of the pipe

Once you have the mass of the fluid (m) and the fluid's velocities at the inlet and outlet, you can calculate the forces applied to the fluid by the pipe in the x and y directions (Fx and Fy) using the force-momentum principle equations provided above.