Momentum Flux and Force of Jets
For a steady control volume, the net external force equals the net outward flux of linear momentum, with pressure and body forces included consistently when they act on the control surface.
Why this shows up in the exam
Forces on pipe bends and nozzles · Water jets striking plates or meshes · Thrust and reaction from fluid streams
Learn the idea
A jet exerts force when its mass flow changes velocity in magnitude or direction. Stopping or turning a stream requires momentum to be removed or redirected each second. The wall or vane receives an equal and opposite force from that rate of momentum change.
🧠 Memory hook: Jet force is momentum changed per second, with direction included.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- F_external = mdot(v_out-v_in) — one-stream steady momentum balance in an inertial frame with vector velocities
- mdot = rho A v — mass-flow rate for a uniform incompressible jet crossing area A
- F_on target = -F_on fluid — Newton's third-law relation after the force on the fluid is found
How to approach it
- 1Choose the fluid as a control volume
- 2Resolve inlet and outlet velocity vectors
- 3Reverse the sign only when reporting force on the target
Common slip-ups that cost marks
- •Using rho A v instead of rho A v squared for a stopped jet force
- •Ignoring unaffected or partially deflected fractions of a stream
- •Dropping vector signs when the jet reverses direction
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A wire 1 m long and cross-sectional area 2 mm^2 extends by 1 mm under a 200 N load. Find Young modulus.
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