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ENGR5002 / Week 3
ENGR217/266 2023 Q A2Past paperCurrent spec2:125 marks30 min

ENGR217/266 Summer 2023 Q A2[VALID] official answers

Water circulates through the horizontal elbow shown in Figure A2 with a constant mass flow rate of 140 kg s−1140\ \mathrm{kg\,s^{-1}}. The water reaching section 2 (the nozzle exit) is discharged at atmospheric pressure. Taking the water density to be ρw=1000 kg m−3\rho_w = 1000\ \mathrm{kg\,m^{-3}}:

Figure A2: the elbow and nozzle combination (section 1 diameter 30 cm, nozzle exit section 2 diameter 16 cm, flow reversed by 180 deg).
Figure A2: the elbow and nozzle combination (section 1 diameter 30 cm, nozzle exit section 2 diameter 16 cm, flow reversed by 180 deg).
Formulas you may need
  • Mass flow rate: m˙=ρAv\dot m = \rho A v, Q=vAQ = vA (on the formula sheet)
  • Bernoulli (no losses, here z1=z2z_1 = z_2): p1ρg+v122g+z1=p2ρg+v222g+z2\dfrac{p_1}{\rho g} + \dfrac{v_1^2}{2g} + z_1 = \dfrac{p_2}{\rho g} + \dfrac{v_2^2}{2g} + z_2 (on the formula sheet)
  • Steady-flow momentum balance (vector, per direction): ∑Fext=∑(m˙v)out−∑(m˙v)in\sum F_{ext} = \sum(\dot m v)_{out} - \sum(\dot m v)_{in} (on the formula sheet)
  • Gauge pressure: pg=p−patmp_g = p - p_{atm} (on the formula sheet)
  1. (a)
    Use the mass conservation principle to obtain the mean normal velocities at section 1 and 2 (the nozzle outlet).
    [4]Third
  2. (b)
    By neglecting viscous losses, write down Bernoulli's equation between section 1 and section 2.
    [4]Third
  3. (c)
    Use the above derived Bernoulli's equation to determine the pressure at section 1.
    [4]2:2
  4. (d)
    Explain why the y component of the force RyR_y required to hold the elbow in place is zero.
    [6]2:2
  5. (e)
    Select an appropriate control volume and apply the momentum equation in the x direction to determine the x component of the force required to hold the elbow.
    [7]