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ENGR5002 / Week 5
ENGR217 2024 Q A1Past paperOld spec ENGR2172:125 marks30 min

ENGR217 Summer 2024 Q A1[VALID]

Answer all parts (a) - (b).

[Data sheet values, not printed in the question: water at 15∘C15^\circ\mathrm{C}, ρ=1000 kg m−3\rho = 1000\ \mathrm{kg\,m^{-3}}, μ=1.14×10−3 N s m−2\mu = 1.14 \times 10^{-3}\ \mathrm{N\,s\,m^{-2}}. The roughness of drawn tubing is not given; a typical textbook value is k≈0.0015k \approx 0.0015 mm.]

Figure A1-1: centrifugal pump with a differential mercury manometer between suction (1) and discharge (2).
Figure A1-1: centrifugal pump with a differential mercury manometer between suction (1) and discharge (2).
Formulas you may need
  • Continuity: Q=vAQ = vA (on the formula sheet)
  • Bernoulli with head loss: v122g+z1+p1ρg=v222g+z2+p2ρg+hL\dfrac{v_1^2}{2g} + z_1 + \dfrac{p_1}{\rho g} = \dfrac{v_2^2}{2g} + z_2 + \dfrac{p_2}{\rho g} + h_L (on the formula sheet)
  • Darcy-Weisbach: hL=f LD v22gh_L = f\,\dfrac{L}{D}\,\dfrac{v^2}{2g}, ff = Darcy factor (on the formula sheet)
  • Reynolds number: Re=ρvDμRe = \dfrac{\rho v D}{\mu} (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 Moody chart is supplied with the paper)
  • Hydrostatics in a manometer: p=p0+ρgzp = p_0 + \rho g z, RD=ρ/ρwRD = \rho/\rho_w (on the formula sheet)
  • Pump head: H=(pρg+v22g+z)out−(pρg+v22g+z)inH = \left(\dfrac{p}{\rho g} + \dfrac{v^2}{2g} + z\right)_{out} - \left(\dfrac{p}{\rho g} + \dfrac{v^2}{2g} + z\right)_{in} (learn this; printed on the 2024 data sheet, not on the current sheets)
  1. (a)
    A farmer wishes to siphon 15∘C15^\circ\mathrm{C} water from a lake 1300 m from a field positioned a distance of 2.5 m below the surface of the lake. What size of drawn tubing should be selected if 0.5 m30.5\ \mathrm{m^3} of water is required each minute? Use the Moody diagram and neglect all losses except that due to wall friction.
    [12]
  2. (b)
    The suction and discharge of a pump are connected to a differential mercury manometer. The diameter of the suction pipe is 250 mm and the diameter of the discharge pipe is 200 mm. The specific gravity of the pumped liquid is S1=0.82S_1 = 0.82 and the specific gravity of mercury is S2=13.6S_2 = 13.6. The manometer reading is H=650H = 650 mm. Determine the pressure head rise across the pump if the discharge is Q=0.12 m3/sQ = 0.12\ \mathrm{m^3/s}. As shown in Figure A1-1, the centreline of the suction pipe to the suction side of the mercury level on the manometer is distance z1z_1 and the centreline of the discharge pipe to the discharge side of the mercury level of the manometer is distance z2z_2.
    [13]