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ENGR5002 / Week 4
ENGR217 2017 Q A2Past paperOld spec ENGR2172:225 marks30 min

ENGR217 Summer 2017 Q A2[VALID] official answers

Answer ALL parts (a) - (d).

[Old data sheet: the friction factor is the Fanning factor f=τw/(12ρu2)f = \tau_w / (\tfrac{1}{2}\rho u^2) with HL=4fLDu22gH_L = \dfrac{4 f L}{D}\dfrac{u^2}{2g}; the current module uses the Darcy factor fD=4ff_D = 4f.]

Figure A2a: tapered circular pipe, 200 mm diameter at inlet (left) reducing to 75 mm at outlet (right).
Figure A2a: tapered circular pipe, 200 mm diameter at inlet (left) reducing to 75 mm at outlet (right).
Figure A2c: Y-pipe with inlet 1 dividing into branches 2 and 3.
Figure A2c: Y-pipe with inlet 1 dividing into branches 2 and 3.
Figure A2d: inclined tube from point 1 up to point 2, 75 m long along the tube, rising 25 m.
Figure A2d: inclined tube from point 1 up to point 2, 75 m long along the tube, rising 25 m.
Formulas you may need
  • Continuity: Q=vAQ = vA, m˙=ρQ=ρAv\dot m = \rho Q = \rho A v (on the formula sheet)
  • Mass balance at a junction: ∑m˙in=∑m˙out\sum \dot m_{in} = \sum \dot m_{out} (on the formula sheet)
  • Energy equation 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=fDLDv22gh_L = f_D \dfrac{L}{D}\dfrac{v^2}{2g} (on the formula sheet)
  • Fanning to Darcy: fD=4fFanningf_D = 4 f_{Fanning} (learn this)
  1. (a)
    Water is flowing from left to right through the tapered circular pipe shown below (see Figure A2a). The mean velocity of the water at the outlet is 4.5 m/s. What is the mean velocity of the water at the inlet?
    [3]
  2. (b)
    Liquid of density 920 kg/m3920\ \mathrm{kg/m^3} is flowing along a cylindrical pipe of internal diameter 250 mm. A container of mass 2.5 kg is used to catch the liquid emerging from the pipe. After a period of 20.0 s the total mass of the container and the liquid is 50.0 kg. Find: (i) The mass flow rate of the liquid (3 marks) (ii) The volume flow rate of the liquid (3 marks) (iii) The mean velocity of flow of the liquid along the pipe (3 marks)
    [9]
  3. (c)
    Water enters the Y-pipe (see Figure A2c) at point 1 at a rate 5.4 L/s, and leaves through branches 2 and 3. The flow rate through branch 3 is 1.8 L/s. Find the mean velocity of the flow through branch 2, whose internal diameter is 50 mm.
    [5]
  4. (d)
    A fluid of density 1180 kg/m31180\ \mathrm{kg/m^3} flows from point 1 to point 2 along the 50 mm internal diameter tube at a velocity of 3.8 m/s (see Figure A2d). The friction factor is f=0.0068f = 0.0068. The gauge pressure at point 2 is to be 2.0×105 N m−22.0 \times 10^5\ \mathrm{N\,m^{-2}}. Find the gauge pressure needed at point 1.
    [8]