MATS2005 Assignment 1 – Fluid Dynamics
• A hardcopy with a cover sheet should be submitted to the assignment box outside the School Office (Room 137, MSE Building E10) by 5pm Friday 2 September
• Assignments submitted after the deadline will receive a 10% of maximum grade penalty for every day late, or part thereof.
• Students are strongly advised to retain a copy of the submission for their records.
Q1. A U-tube manometer contains mercury of density 13,600 kg/m3, and oil.
(a) When both ends of the tube are open to the atmosphere, h1 = 0.25 m and ?h = 1.6 cm. Calculate the density of the oil.
(b) The open end of the left leg is sealed and is pressurized to a gauge pressure P, which causes the level of the free surface of the oil in the left leg to fall 5 mm. Calculate the gauge pressure P.
Q2. Based on the momentum balance, develop expressions of velocity and shear stress for the flow of a fluid between two parallel plates (length L and width W) inclined at an angle of ? to the gravity direction and separated by a distance of 2?. The overall pressure drop over the plate is ?P. Calculate the volume flow rate.
Q3. Air at 300 K is flowing through a horizontal tube of inner diameter 2 cm. The local flow velocity measured at a radius of 5 mm from the tube centerline is 0.9 m/s.
(a) The rate of pressure drop in the flowing air.
(b) The average linear velocity of the flow.
(c) The shear stress exerted on the tube by the air.
At 300 K the density and viscosity of air are, respectively, 1.2 kg/m3 and 1.85 ? 10-5 Pa·s.
Q4. Calculate the pressure drop required to give a flow rate of water of 50 kg/s through a 500m length of 0.3m I.D. pipe of relative roughness 1.8?10-4.
The density and viscosity of water at 300K are 1000kg/m3 and 8.6?10-4 Pa.s.
Q5. A lead shot of diameter 3 mm is fired upward into still air at 300 K over open water.
a) The drag force that the shot experiences as it leaves the gun barrel at a velocity of 150 m/s
b) The terminal velocity that it attains when it falls through the still air
c) The terminal velocity that it attains when it falls through the still water
Density of lead 11,340 kg/m3, ? (air) 1.177 kg/m3, ? (air) 1.85?10-5 Pa?s, ???water) 1000 kg/m3, ? ?water) 8.57?10-4 Pa?s.
Q6. Water at 300 K is being pumped from the lower to the higher reservoir through a pipe of 0.2 m diameter and equivalent length 60 m. The absolute roughness of the pipe is 2 mm. Calculate the power rating of the pump required to pump the water at a flow rate of 0.2m3/s. The efficiency of the pump is 75%.
The density and viscosity of water at 300K are 1000kg/m3 and 8.6?10-4 Pa.s