ENGR217 2025 Q A1 (ENGR5002)

ENGR217 2025 Q A1Past paperOld spec ENGR2172:125 marks30 min

Answer all parts (a) - (c).

Formulas you may need

Bernoulli with head loss: $\dfrac{v_1^2}{2g} + z_1 + \dfrac{p_1}{\rho g} = \dfrac{v_2^2}{2g} + z_2 + \dfrac{p_2}{\rho g} + h_L$ (on the formula sheet)
Darcy-Weisbach: $\Delta p = f\,\dfrac{L}{D}\,\dfrac{\rho v^2}{2}$ , $h_L = f\,\dfrac{L}{D}\,\dfrac{v^2}{2g}$ ( $f$ = Darcy factor) (on the formula sheet)
Reynolds number: $Re = \dfrac{\rho v D}{\mu} = \dfrac{vD}{\nu}$ ; laminar below about 2300, turbulent above 4000 (on the formula sheet)
Moody chart / Colebrook: $\dfrac{1}{\sqrt f} = -2\log_{10}\left(\dfrac{k/D}{3.7} + \dfrac{2.51}{Re\sqrt f}\right)$ (learn this; the Moody chart is supplied with the paper)
Hagen-Poiseuille: $\Delta p = \dfrac{8\mu L Q}{\pi R^4}$ , i.e. $Q = \dfrac{\pi\,\Delta p\,R^4}{8\mu L}$ (on the formula sheet)
Continuity: $Q = vA$ (on the formula sheet)

(a)
Water at $12^\circ\mathrm{C}$ is supplied to a 40 mm diameter steel pipe at 9 bar gauge pressure. The pipe is 125 m long, the roughness is $k = 0.02$ mm, and at the end of the pipe the water is discharged to atmosphere. Estimate the volume flow rate of the water. (Kinematic viscosity for the water is $\nu = 1.22 \times 10^{-6}\ \mathrm{m^2/s}$ ).
f (Darcy) =-
Q =L/s
[15]
(b)
Diesel fuel flows along a pipe 12 m long, whose bore (internal diameter) is 8 mm. The density and viscosity of the fuel are $850\ \mathrm{kg/m^3}$ and $1.8 \times 10^{-3}\ \mathrm{N\,s/m^2}$ respectively. If the pressure drop over the length of the pipe $1.5\ \mathrm{kN/m^2}$ , estimate the volume flow rate of fuel along the pipe. (Hint: use Poiseuille's equation.)
Q =m^3/s
[6]Third
(c)
Hot water at $50^\circ\mathrm{C}$ is flowing along a pipe 800 mm diameter at a mean speed of 2.3 m/s. At this temperature the kinematic viscosity of the water is $\nu = 5.55 \times 10^{-7}\ \mathrm{m^2/s}$ . Will the flow be laminar or turbulent?
Re =-
[4]Third