ENGG2500 Chap.5 Linear Momentum and Flow Forces
Linear Momentum and Flow Forces
Linear momentum applies Newton's second law to a flowing control volume. Pressure, weight and wall or support interactions form the external force system, while mass flow carries velocity vectors across the boundary. Continuity often supplies speeds and energy may supply a missing magnitude before momentum determines jet thrust, nozzle force or bend reaction. The requested body controls the final sign.
A complete solution fixes axes and a reference frame, resolves every inlet and outlet velocity, uses pressure forces in their inward directions and distinguishes force on fluid from the equal-and-opposite force on hardware.
What this chapter covers
- 01
Control-volume momentum balance
- 02
Pressure and body forces
- 03
Jets and stationary plates
- 04
Nozzle thrust
- 05
Pipe-bend reactions
- 06
Coupled energy and momentum problems
Worked example · free
Nozzle force with atmospheric discharge
- 1Use continuity for 4.72 and 18.86 m/s section speeds. These marks are not a published university marking scheme.
- 1Mass flow is 30.0 kg/s.
- 1Inlet pressure force is 1018 N and momentum change is 424 N.
- 1Nozzle-on-fluid force is 594 N upstream.
Key terms
- Momentum flux
- Momentum flux is the rate at which flowing mass carries vector momentum across a surface.
- Pressure force
- Pressure force acts inward on a control surface.
- Reaction force
- A reaction force is the support interaction required to satisfy the force balance.
- Thrust
- Thrust is a force created by changing a stream's momentum and pressure forces.
Linear Momentum and Flow Forces FAQ
Why is momentum a vector calculation?
Momentum contains velocity, which has direction as well as magnitude. A bend can keep speed constant while changing momentum because the velocity direction rotates. Resolve inlet and outlet vectors into chosen axes and preserve signed components until the force magnitude and direction are reported.
How do pressure forces enter the control volume?
Pressure acts normal and inward on each control surface. Gauge pressure is often convenient because common atmospheric forces cancel. Draw the arrows first, then assign component signs from the geometry. Do not attach a pressure force automatically in the flow direction at every opening.
Why reverse the final force sometimes?
The momentum equation often solves the wall or nozzle force acting on the fluid. A support question may ask for the fluid force on the hardware, which is the equal-and-opposite interaction. The requested free body determines which member of that action-reaction pair is reported.
Can a flow have force when inlet and outlet speeds match?
Yes. Momentum depends on the velocity vector, so a bend changes momentum even when speed is constant. Pressure forces and weight can also require a reaction. Resolve the inlet and outlet directions into components rather than comparing only their speed magnitudes.
When should weight be included in momentum balance?
Include the weight of fluid inside the control volume when its component is not negligible relative to pressure and momentum forces, especially for large vertical devices. Estimate the contained fluid volume and direction. Do not add the hardware weight unless the requested free body includes the hardware and supports.
How does a moving vane change a jet problem?
The mass rate striking a moving vane depends on jet speed relative to the vane. The outlet velocity must then be transformed back to the fixed frame before calculating momentum flux. Using the stationary-plate mass rate overpredicts both force and mechanical power transferred to the vane.
What is pressure thrust at an outlet?
If outlet static pressure differs from the surrounding pressure, the pressure acting over the outlet area contributes to thrust. A free jet discharging at ambient pressure has zero gauge outlet pressure and no such correction. State the pressure reference so that atmospheric effects are not counted twice.
Why use continuity before momentum?
Momentum flux needs mass flow and velocity at every opening. Continuity links those section quantities and can reveal a missing branch flow or speed before the force balance begins. Solving that scalar bookkeeping first keeps a mass-conservation error from being mistaken for an incorrect pressure or reaction force.
Exam move
Make the free-body diagram do the sign work. Draw a fixed control volume, choose positive axes and mark outward normals at every opening. Use continuity to calculate mass flow and average velocities, and use energy first if a velocity magnitude is missing. Add pressure arrows inward on the control surfaces, include fluid weight when it matters and label the unknown wall or support interaction as force on the fluid.
Write one momentum equation per component and keep velocity signs from the vector sketch. Once the algebra gives force on fluid, read the question again and reverse it only if force on the pipe, nozzle, plate or support is requested.
Convert components into magnitude and direction, then test limiting cases: no turning should remove transverse force, stopping a component should require force opposite that component, and reversing it should require a larger change. For moving-vane questions, compute relative incident flow and return outlet velocities to the fixed frame before the balance.