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04-BS-7 · Undated paper

Question 9 of 13: Pressure Drop Along a CANDU Fuel Bundle Annulus

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 9: Pressure Drop Along a CANDU Fuel Bundle Annulus (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
Pressure tube ID104.0 mm
Fuel rod OD13.1 mm
Number of rods37
Bundle length495 mm
Coolant density712 kg/m³
Coolant viscosity9.0×10⁻⁵ N·s/m²
Coolant flow rate24 kg/s

Find. The pressure drop over one fuel bundle length.

37 fuel rods (13.1 mm) inside a 104.0 mm pressure tube (schematic)
Coolant flows through the annular gaps between the 37 rods and the pressure tube; friction acts on both the tube's inner wall and every rod's outer wall.

Approach. Treat the rod bundle as flow through a non-circular annulus: compute the net flow area (tube minus rods) and the hydraulic diameter (using the full wetted perimeter of both the tube wall and all 37 rods), then apply the Darcy–Weisbach relation with a Moody-chart friction factor.

  1. Net flow area. $$ A_{flow} = \frac{\pi}{4}D_{tube}^2 - n\frac{\pi}{4}d_{rod}^2 = \frac{\pi}{4}(0.104)^2 - 37\frac{\pi}{4}(0.0131)^2 \approx 3.508\times10^{-3}\ \text{m}^2 $$
  2. Hydraulic diameter. Wetted perimeter $P = \pi D_{tube} + n\pi d_{rod} = \pi(0.104)+37\pi(0.0131) \approx 1.849$ m: $$ D_h = \frac{4A_{flow}}{P} = \frac{4(3.508\times10^{-3})}{1.849} \approx 7.59\ \text{mm} $$
  3. Velocity and Reynolds number. $$ V = \frac{\dot m}{\rho A_{flow}} = \frac{24}{(712)(3.508\times10^{-3})} \approx 9.61\ \text{m/s} $$ $$ Re = \frac{\rho V D_h}{\mu} = \frac{(712)(9.61)(0.00759)}{9.0\times10^{-5}} \approx 5.77\times10^5 $$
  4. Friction factor and pressure drop. Treating the Zircaloy surfaces as hydraulically smooth (Moody chart, smooth curve), $f \approx 0.0128$: $$ \Delta p = f\frac{L}{D_h}\frac{\rho V^2}{2} = (0.0128)\left(\frac{0.495}{0.00759}\right)\frac{(712)(9.61)^2}{2} $$ $$ \boxed{\Delta p \approx 27.5\ \text{kPa}} $$
QuantityResult
Net flow area3.51×10⁻³ m²
Hydraulic diameter7.59 mm
Coolant velocity9.61 m/s
Pressure drop per bundle27.5 kPa
Check: as in Question 8, no explicit surface roughness is given for the Zircaloy pressure tube/fuel rods, so the smooth-pipe Moody curve is used, consistent with the very smooth as-manufactured finish of Zircaloy cladding.