Drain-Cleaning Nozzle Thrust: 04-BS-7, May 2014, Q8

Question 8 — Drain-Cleaning Nozzle Thrust (5 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given.

Quantity	Value
Orifice diameter (all 7)	2 mm
Supply pressure	6 MPa
Side-jet angle from centreline	26°
Number of side jets	6 (angled rearward, propelling the nozzle forward)
Number of front jets	1 (fires forward, opposing the pull)

Find. The net axial (pulling) force developed by the nozzle.

Fig. Q8 — drain-cleaning nozzle: the six rearward-angled side jets (26° from the centreline) give a net forward reaction that pulls the hose into the drain, partly offset by the forward-firing front jet.

Approach. Each orifice is a small free jet with velocity from Bernoulli (approach velocity neglected); the six rearward-angled side jets each contribute a forward thrust reaction proportional to cos(26°), opposed by the single forward-firing front jet's full reaction.

Jet velocity and thrust per orifice. $$V=\sqrt{{\frac{{2p}}{{\rho}}}}=\sqrt{{\frac{{2\times6\times10^6}}{{1000}}}}=109.5\text{{ m/s}}$$ $$a=\frac{{\pi}}{{4}}(0.002)^2=3.142\times10^{{-6}}\text{{ m}}^2,\quad Q_j=aV=3.44\times10^{{-4}}\text{{ m}}^3/\text{{s}}$$ $$F_{{jet}}=\rho Q_j V = 1000\times3.44\times10^{{-4}}\times109.5 = 37.7\text{{ N (per orifice)}}$$
Front jet (retarding, full axial reaction). $$F_{{front}} = F_{{jet}} = 37.7\text{{ N, opposing insertion}}$$
Side jets (six, rearward at 26° — radial components cancel by symmetry, axial component drives the nozzle forward). $$F_{{side,axial}} = 6\,F_{{jet}}\cos26^\circ = 6\times37.7\times0.8988 = 203.3\text{{ N}}$$
Net pulling force. $$F_{{net}} = F_{{side,axial}}-F_{{front}} = 203.3-37.7 = \boxed{{165.6\text{{ N}}}}$$

Quantity	Result
Jet velocity (each orifice)	109.5 m/s
Thrust per orifice	37.7 N
Net forward (pulling) force	165.6 N

Topic: Momentum/thrust of multiple free jets (rocket-nozzle analogy).

Key relations: free-jet velocity V=√(2p/ρ); thrust reaction F=ρQV; only the axial component of an angled jet's thrust contributes to net propulsion.

Why this works: Newton's third law — each jet exiting the nozzle pushes the nozzle body in the opposite direction. Six jets fired rearward and outward at a shallow 26° angle both scour the drain walls (radial component) and drive the nozzle forward (axial component); the front jet, firing straight ahead to clear debris, necessarily costs some of that thrust back.

Common pitfall: forgetting to resolve the side-jet thrust into its axial component (using the full 37.7 N instead of 37.7cos26°), or forgetting to subtract the front jet's opposing reaction.

Source: White, Fluid Mechanics, 8th ed., §3.9 (momentum equation, jet propulsion).

Question 8 of 13: Drain-Cleaning Nozzle Thrust

Question 8 — Drain-Cleaning Nozzle Thrust (5 marks)