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04-BS-7 · May 2016

Question 7 of 13: Jet Force vs. Static Pressure Force on a Nozzle Plate

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

04-BS-7 Mechanics of Fluids — May 2016 (National Examinations, three hours, closed book). Section A (Calculative) offers 9 questions and instructs "do seven"; Section B (Analytical/Graphical) offers 4 questions and instructs "do three." Every question is answered below (13 of 13), so students can use the full paper as a study resource. Constants used throughout (from the paper's own Constants page): g = 9.81 m/s², patm = 100 kPa (an atmospheric head of 10 m of water is specified separately for Question 1), ρwater = 1000 kg/m³, SGglycerine = 1.26, SGmercury = 13.56, ρconcrete = 2400 kg/m³, ρair = 1.19 kg/m³ (20°C) / 1.21 kg/m³ (15°C), μwater = 1.0×10⁻³ N·s/m², Rair = 287 J/kg·K.

Reference texts: F. M. White, Fluid Mechanics, 8th ed. (McGraw-Hill) — fluid statics and manometry (Ch. 2), hydrostatic forces and the middle-third rule (Ch. 2), dimensional analysis and drag (Ch. 5, 7), pipe friction and the Moody/Colebrook relation (Ch. 6), control-volume momentum (Ch. 3); B. R. Munson et al., Fundamentals of Fluid Mechanics — jets, orifices, and streamline patterns (Ch. 5, 8); J. D. Anderson, Fundamentals of Aerodynamics — wave/compressibility drag divergence (Ch. 5) for the Boeing 747 wind-tunnel chart used in Question 9.

Question 7: Jet Force vs. Static Pressure Force on a Nozzle Plate (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.

QuantityValue
Nozzle diameter d30 mm
Differential head h2 m
Water density ρ1000 kg/m³

Find. (a) FA, momentum force of the free jet on the plate; (b) FB, static pressure force with flow stopped; whether FA = FB.

Approach. Find the jet exit velocity from Bernoulli (head h converts fully to velocity head), then compute (a) the momentum-flux force of the flowing jet striking a plate held clear of the nozzle, and (b) the static pressure force with the plate sealing the nozzle and flow stopped (Bernoulli with V=0 at the plate).

  1. Jet exit velocity and area. $$V=\sqrt{2gh}=\sqrt{2(9.81)(2)}=6.264\ \text{m/s}, \qquad A=\frac{\pi}{4}(0.030)^2=7.069\times10^{-4}\ \text{m}^2$$
  2. (a) Force of the flowing jet (momentum flux, plate a short distance away, flow continues past the plate radially). $$F_A=\rho Q V=\rho A V^2 = 1000(7.069\times10^{-4})(6.264^2)=\boxed{27.74\ \text{N}}$$
  3. (b) Force with the plate sealing the nozzle (no flow, static pressure only). $$p=\rho g h = 1000(9.81)(2)=19\,620\ \text{Pa}, \qquad F_B = pA = 19\,620(7.069\times10^{-4})=\boxed{13.87\ \text{N}}$$
  4. Compare. $F_A/F_B = \rho AV^2/(\rho gh\,A) = V^2/(gh) = 2gh/gh = 2$, so the flowing-jet force is exactly twice the static blocked-flow force — the two forces are NOT the same.
QuantityResult
FA (flowing jet on plate)27.74 N
FB (static, flow stopped)13.87 N
Ratio FA:FB2 : 1