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04-BS-7 · Undated paper

Question 8 of 13: Friction Head Loss in a Flexible Corrugated Discharge Pipe

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

Notes on this paper

04-BS-7 Mechanics of Fluids — undated sitting, identified as May 2019 (National Examinations, three hours, closed book). Section A (Calculative) offers 9 questions and instructs “do seven”; Section B (Analytical) offers 4 questions and instructs “do three.” A complete paper is any 10 of the 13, each worth 5 marks. Every question is answered below (13 of 13) so the set can be used as a full study resource. Constants used throughout (from the paper's own Constants page, p.12): g = 9.81 m/s², patm = 100 kPa, ρwater = 1000 kg/m³, SGbenzene = 0.90, SGmercury = 13.56, SGcarbon tetrachloride = 1.59, ρair = 1.19 kg/m³ (20°C), μwater = 1.0×10⁻³ N·s/m², μair = 1.8×10⁻⁵ N·s/m².

Reference texts: F. M. White, Fluid Mechanics, 8th ed. (McGraw-Hill) — fluid statics and manometry (Ch. 2), hydrostatic forces on plane surfaces (Ch. 2), the Bernoulli/continuity pair and orifice flow (Ch. 3), the linear-momentum equation for moving vanes (Ch. 3), pipe friction and the Moody/Colebrook relation (Ch. 6), boundary layers and drag (Ch. 7), capillary rise (Ch. 1), high-lift devices and aircraft wing aerodynamics (J. D. Anderson, Fundamentals of Aerodynamics, Ch. 4–5).

Question 8: Friction Head Loss in a Flexible Corrugated Discharge Pipe (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
Inside diameter, D32 mm
Overall length, L2.85 m
Flow rate, Q96 L/min
Fluidwater, μ = 1.0×10⁻³ N·s/m²

Find. The friction head loss over the full pipe length.

Check: no relative roughness is given for this pipe on the exam's Constants/Moody pages, so — per the paper's own Note 4 ("if in doubt, make an assumption and state it clearly") — this solution treats the flow surface as hydraulically smooth (the same idealisation used for the discharge pipe's straight-run friction elsewhere on this paper) and reads the friction factor from the smooth-pipe curve of the Moody diagram at the computed Reynolds number.

Approach. Compute the mean velocity from continuity, form the Reynolds number, read the (assumed-smooth) friction factor from the Moody chart, then apply the Darcy–Weisbach relation.

  1. Mean velocity. $A = \tfrac{\pi}{4}(0.032)^2 = 8.04\times10^{-4}$ m², $Q=1.6\times10^{-3}$ m³/s: $$ V = \frac{Q}{A} = \frac{1.6\times10^{-3}}{8.04\times10^{-4}} \approx 1.99\ \text{m/s} $$
  2. Reynolds number. $$ Re = \frac{\rho V D}{\mu} = \frac{(1000)(1.99)(0.032)}{1.0\times10^{-3}} \approx 6.37\times10^4 $$
  3. Friction factor (Moody chart, smooth-pipe curve). At this Reynolds number the smooth curve gives: $$ f \approx 0.0198 $$
  4. Darcy–Weisbach head loss. $$ h_L = f\frac{L}{D}\frac{V^2}{2g} = (0.0198)\left(\frac{2.85}{0.032}\right)\frac{(1.99)^2}{2(9.81)} $$ $$ \boxed{h_L \approx 0.356\ \text{m}} $$
QuantityResult
Mean velocity1.99 m/s
Reynolds number6.37×10⁴
Friction factor (smooth)0.0198
Head loss over 2.85 m0.356 m