Question

Q5. Sketching a suitable control volume, show that the velocity profile V(r) for steady, fully laminar flow in a horizontal pipe is given by V(r)- whereis is the pressure drop per unit length of pipe, R is the pipe radius and u the dynamic viscosity of the fluid. (10 marks) Thereafter develop Poiseuille's law for the volume flow rate O in the form SuL (10 marks) Hence show that the head loss h is given by where Vis the mean velocity, ρ is the fluid density and g the gravitational acceleration. (5 marks) 06. (a) Brielfy describe Reynolds' pipe flow experiment, indicating his major observations and clearly reporting his conclusions in relation to the description of laminar, transitional and turbulent flow (6 marks) (b) A pipe inclined to the horizontal at an angle of 60° conveys a liquid upwards through a height of 10 m. The diameter of the pipe reduces from 20 mm at its inlet to 10 mm at its outlet. At the mean diameter of the pipe the velocity is 5.0 m/s. The density of the liquid is 840 kg/m3 and its viscosity 0.005 Ns/m2 Calculate (i) (ii) (iii) (iv) (v) the mean diameter of this pipe and the volume flow rate, the inlet and outlet velocities, the Reynolds number at the mean diameter, the head loss through the pipe assuming a the pressure drop across the pipe. (3 marks) (4 marks) (3 marks) (4 marks) (5 marks) smooth internal wall, and

Answer 1

h