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ENGR5002 / Week 4
ENGR217 2018 Q B1Past paperOld spec ENGR2172:225 marks30 min

ENGR217 Summer 2018 Q B1[VALID] official answers

Answer ALL parts (a) - (c).

[A Moody diagram is needed for (b). The old data sheet defines the Fanning friction factor, HL=4fLDu22gH_L = \dfrac{4 f L}{D}\dfrac{u^2}{2g}; the current module uses the Darcy factor fD=4ff_D = 4f.]

Formulas you may need
  • Reynolds number: Re=ρvDμRe = \dfrac{\rho v D}{\mu}; laminar Re<2400Re < 2400, turbulent Re>4000Re > 4000 (on the formula sheet)
  • Darcy-Weisbach: Δp=fDLDρv22\Delta p = f_D \dfrac{L}{D}\dfrac{\rho v^2}{2} (on the formula sheet)
  • Moody chart / Colebrook: 1fD=−2log⁡10(k/D3.7+2.51RefD)\dfrac{1}{\sqrt{f_D}} = -2\log_{10}\left(\dfrac{k/D}{3.7} + \dfrac{2.51}{Re\sqrt{f_D}}\right) (learn this; a Moody chart would be supplied)
  • Hagen-Poiseuille: Q=Δp πR48μLQ = \dfrac{\Delta p\, \pi R^4}{8 \mu L}, equivalently Δp=32μLvD2\Delta p = \dfrac{32 \mu L v}{D^2} (on the formula sheet)
  • Fanning to Darcy: fD=4fFanningf_D = 4 f_{Fanning} (learn this)
  1. (a)
    A pipeline 1200 mm in diameter carries a flow of methane gas at 15∘C15^\circ\mathrm{C} and gauge pressure 3.5 bar. The density of the gas is 2.70 kg/m32.70\ \mathrm{kg/m^3} and its viscosity is 1.15×10−5 N s/m21.15 \times 10^{-5}\ \mathrm{N\,s/m^2}. The mean velocity of flow of the gas is 0.90 m/s. Is the flow laminar or turbulent?
    [5]
  2. (b)
    Find the friction factor for the condition given above, and estimate the pressure drop in a 250 m length of the pipeline. The roughness value of the inner surface of the pipeline is k=0.35k = 0.35 mm.
    [10]
  3. (c)
    Diesel fuel flows along a pipe 6 m long, whose bore (internal diameter) is 5 mm. The density and viscosity of the fuel are 850 kg/m3850\ \mathrm{kg/m^3} and 1.8×10−3 N s/m21.8 \times 10^{-3}\ \mathrm{N\,s/m^2} respectively. If the pressure drop over the length of the pipe is 1.3 kN/m21.3\ \mathrm{kN/m^2}, estimate the volume flow rate of fuel along the pipe. (Hint: Poiseuille's equation: Q=ΔP πR4/(8μL)Q = \Delta P\, \pi R^4 / (8 \mu L).)
    [10]