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ENGR5002 / Week 4
ENGR217/266 2021 Q1Past paperCurrent spec2:225 marks30 min

ENGR217/266 Summer 2021 Q1[VALID]

Answer all parts (a) - (c).

[Data Book values, not printed in the question: ethyl alcohol at 15∘C15^\circ\mathrm{C}, ρ=789 kg m−3\rho = 789\ \mathrm{kg\,m^{-3}}, μ=1.323×10−3 N s m−2\mu = 1.323 \times 10^{-3}\ \mathrm{N\,s\,m^{-2}}. A Moody diagram is needed for (b).]

Formulas you may need
  • Reynolds number: Re=ρvDμ=vDνRe = \dfrac{\rho v D}{\mu} = \dfrac{vD}{\nu} (on the formula sheet)
  • Pipe-flow regimes: laminar Re<2400Re < 2400, turbulent Re>4000Re > 4000 (on the formula sheet)
  • Darcy-Weisbach: Δp=fLDρv22\Delta p = f \dfrac{L}{D} \dfrac{\rho v^2}{2}, hL=fLDv22gh_L = f \dfrac{L}{D}\dfrac{v^2}{2g} (on the formula sheet)
  • Moody chart / Colebrook: 1f=−2log⁡10(k/D3.7+2.51Ref)\dfrac{1}{\sqrt f} = -2\log_{10}\left(\dfrac{k/D}{3.7} + \dfrac{2.51}{Re\sqrt f}\right) (learn this; the chart itself would be supplied)
  • Fanning to Darcy: fDarcy=4fFanningf_{Darcy} = 4 f_{Fanning}, old sheet HL=4fFLu22gDH_L = \dfrac{4 f_F L u^2}{2 g D} (learn this)
  • Hagen-Poiseuille: Q=πR4Δp8μLQ = \dfrac{\pi R^4 \Delta p}{8 \mu L}, Δp=32μLvD2\Delta p = \dfrac{32 \mu L v}{D^2} (on the formula sheet)
  • Flow rate: Q=vAQ = vA (on the formula sheet)
  1. (a)
    A pipeline 600 mm in diameter carries a flow of ethyl alcohol at 15∘C15^\circ\mathrm{C} and gauge pressure 3.5 bar. The mean velocity of flow of the liquid is 4.50 m s−14.50\ \mathrm{m\,s^{-1}}. Referring as appropriate to the Data Book please estimate if the flow is laminar or turbulent. Please comment further on the value obtained.
    [5]
  2. (b)
    Find the friction factor for the condition given above, and estimate the pressure drop in a 125 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)
    An n-Octane liquid, flows along a 1500 m long pipe, whose bore (internal diameter) is 0.2 m. The values for the density and dynamic viscosity of the fuel are 702 kg m−3702\ \mathrm{kg\,m^{-3}} and 0.582×10−3 N s m−20.582 \times 10^{-3}\ \mathrm{N\,s\,m^{-2}} respectively. If the pressure drop over the length of the pipe 2.0 N m−22.0\ \mathrm{N\,m^{-2}}, estimate the volume flow rate of fuel along the pipe. (Hint: since the bore is small, assume the flow is laminar and use Poiseuille's equation (Q=Δp πR4/(8μl)Q = \Delta p\,\pi R^4 / (8 \mu l)) to find the flow rate. Then find the flow velocity, and hence the Reynolds number, to check that the flow is indeed laminar.)
    [10]