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04-BS-7 · May 2017

Question 8 of 13: CANDU Fuel Bundle — Coolant Pressure Drop

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

Notes on this paper

04-BS-7 Mechanics of Fluids — National Examination, 2017-May. Three (3) hours duration, closed book. Section A (Calculative, 9 questions, do 7) and Section B (Graphical & Analytical, 4 questions, do 3); every question is answered below regardless of the exam's "do N of M" instruction, so the set is a complete study resource.

Reference texts: White, F.M., Fluid Mechanics (8th ed.) — fluid statics and capillarity (Ch. 2), integral analysis and buoyancy (Ch. 3), viscous flow in ducts, pipe friction and the Moody chart (Ch. 6), flow past immersed bodies and drag (Ch. 7), open-channel flow and the hydraulic jump (Ch. 10).

Check — assumptions used across this paper:
  • Q2's figure shows the vertical leaf of the gate rising above the free surface, so water acts over the full depth x = 2.0 m; both "0.3 m" dimensions locate the centre of gravity (0.3 m right of the vertical leaf, 0.3 m above the arm). Reservoir water also fills the space beneath the 1.2 m arm (the vertical lines below O are dimension extension lines, not a wall), so the arm carries uplift at pressure ρgx, and the arm tip bears up against a lip on the spillway crest — the gate can only open by rotating clockwise, vertical leaf toward the spillway.
  • Q4's flow coefficient K ≈ 0.69 is read from the attached VDI chart on the Do/D1 = 0.50 curve (third from the top, the one that levels off at 0.62) at the approach Reynolds number R ≈ 2550. The printed curve gives 0.695 at R = 2000 and 0.684 at R = 3000; a reading of 0.68–0.70 moves the answer by only ±0.3 kPa.
  • Q7 and Q8 friction factors are obtained from the Colebrook–White/Haaland equation the Moody chart itself plots (smooth-wall case, as both problems specify or imply smooth surfaces).
  • Q9's sphere drag coefficient vs. Reynolds number is obtained from the Schiller–Naumann correlation $C_D=\tfrac{24}{Re}\left(1+0.15\,Re^{0.687}\right)$, which reproduces the published sphere-drag curve (the same curve reprinted in the attachment) to within a few percent for $Re<1000$ — used here because the resulting Reynolds number (≈19–20) is well above the range where the simple Stokes'-law formula ($C_D=24/Re$) alone is valid.

Question 8: CANDU Fuel Bundle — Coolant Pressure Drop (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. Pressure-tube I.D. $D_{tube}=104.0\ \text{mm}$; 37 fuel rods, O.D. $d_{rod}=13.1\ \text{mm}$ each; bundle length $L=495\ \text{mm}$; coolant $\rho=712\ \text{kg/m}^3$, $\mu=9.0\times10^{-5}\ \text{kg/m\,s}$; mass flow rate $\dot m=24\ \text{kg/s}$; spacers, entrance/exit losses neglected (smooth surfaces assumed, per the check note).

Find. Pressure drop across one fuel bundle.

Approach. Treat the coolant channel as the annular flow area between the pressure-tube bore and the 37 rod surfaces; compute its hydraulic diameter, Reynolds number and (smooth-surface) friction factor, then apply Darcy–Weisbach.

  1. Flow area (tube bore minus 37 rods). $A_{tube}=\tfrac\pi4(0.104)^2=8.495\times10^{-3}\ \text{m}^2$; $A_{rods}=37\times\tfrac\pi4(0.0131)^2=4.987\times10^{-3}\ \text{m}^2$: $$A_{flow}=A_{tube}-A_{rods}=3.508\times10^{-3}\ \text{m}^2$$
  2. Wetted perimeter and hydraulic diameter. $P_{wet}=\pi D_{tube}+37\pi d_{rod}=\pi(0.104+37\times0.0131)=1.849\ \text{m}$: $$D_e=\frac{4A_{flow}}{P_{wet}}=\frac{4\times3.508\times10^{-3}}{1.849}=\boxed{7.587\ \text{mm}}$$
  3. Velocity and Reynolds number. $V=\dot m/(\rho A_{flow})=24/(712\times3.508\times10^{-3})=9.609\ \text{m/s}$; $\nu=\mu/\rho=1.264\times10^{-7}\ \text{m}^2/\text{s}$: $$Re=\frac{D_eV}{\nu}=\frac{0.007587\times9.609}{1.264\times10^{-7}}=\boxed{5.77\times10^5}$$
  4. Friction factor (smooth surfaces, Haaland) and pressure drop. $f=\left[-1.8\log_{10}(6.9/Re)\right]^{-2}=0.01274$: $$\Delta p=f\frac{L}{D_e}\left(\frac{\rho V^2}{2}\right)=0.01274\times\frac{0.495}{0.007587}\times\frac{712\times9.609^2}{2}=\boxed{27.32\ \text{kPa}}$$
QuantityValue
Flow (annular) area3.508×10⁻³ m²
Hydraulic diameter, $D_e$7.59 mm
Coolant velocity, V9.61 m/s
Reynolds number, Re5.77×10⁵
Pressure drop over the bundle27.32 kPa