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ENGR5002 / Week 3
ENGR217/266 2022 Q A2Past paperCurrent spec2:225 marks30 min

ENGR217/266 Summer 2022 Q A2[VALID]

Water flows through a horizontal tee pipe junction as shown in Figure A2-1. The pipe containing section (1) is orthogonal to the pipe joining sections (2) and (3). Each of the three pipes joining the junction has an internal diameter of 2.5 m. The water density can be assumed to be ρw=1000 kg m−3\rho_w = 1000\ \mathrm{kg\,m^{-3}}. The flow rate through section (3) is Q3=55 m3/sQ_3 = 55\ \mathrm{m^3/s}, the average velocity at section (1) is V1=5.5 m/sV_1 = 5.5\ \mathrm{m/s} where the pressure is p1=450 kPap_1 = 450\ \mathrm{kPa}.

Figure A2-1: horizontal tee junction; inflow at section (1), outflow at (3), section (2) on the y axis.
Figure A2-1: horizontal tee junction; inflow at section (1), outflow at (3), section (2) on the y axis.
Formulas you may need
  • Flow rate: Q=vAQ = vA, A=πD2/4A = \pi D^2/4 (on the formula sheet)
  • Mass balance: ∑m˙in−∑m˙out=dmCVdt\sum \dot m_{in} - \sum \dot m_{out} = \dfrac{dm_{CV}}{dt}, m˙=ρQ\dot m = \rho Q (on the formula sheet)
  • Bernoulli (no losses, hL=0h_L = 0): 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)
  1. (a)
    Determine the water volume flow rate Q1Q_1 at section (1) and the average velocity V3V_3 at section (3).
    [6]
  2. (b)
    Use a mass balance to find the water volume flow rate Q2Q_2 at section (2) and the corresponding average velocity V2V_2.
    [5]
  3. (c)
    Is the flow directed towards the positive or the negative y direction at (2)?
    [4]
  4. (d)
    State the hypotheses that should be verified by the fluid flow for the Bernoulli's equation to be applicable.
    [4]
  5. (e)
    Assuming that the hypotheses behind Bernoulli's equation are verified by the flow in the junction (see question A2-(d)), consider two streamlines joining respectively section (1) with sections (2) and (3) to determine the pressure at (2) and at (3).
    [6]