Assignment 3 odd
- 1. INDIAN INSTITUTE OF SPACE SCIENCE AND TECHNOLOGY THIRUVANANTHAPURAM DEPARTMENT OF AEROSPACE ENGINEERING AE213 FLUID MECHANICS – ASSIGNMENT – 3 Last date of submission : 5 November 2012 1. A light liquid (ρ = 950 kg/m3 ) flows at an average velocity of 10 m/s through a horizontal smooth tube of diameter 5 cm. The fluid pressure is measured at 1-m intervals along the pipe, as follows: x, m 0 1 2 3 4 5 6 p, kPa 302 275 257 242 228 214 200 Estimate (a) the average wall shear stress, in Pa, and (b) the wall shear stress in the fully developed region of the pipe. 2. Glycerin at flows upward in a vertical 75-mm-diameter pipe with a centerline velocity of 1.0 m/s. Determine the head loss and pressure drop in a 10-m length of the pipe. 3. Oil, with ρ = 890 kg/m3 and µ = 0.06 kg/(m s), is to be pumped through 1 km of straight horizontal pipe with a power input of 1 kW. What is the maximum possible mass flow rate, and corresponding pipe diameter, if laminar flow is to be maintained? 4. For the configuration shown in figure below, all parameters are constant except the upper tank depth Z(t). Find an expression for the flow rate Q(t) as a function of Z(t). Set up a differential equation, and solve for the time t0 to drain the upper tank completely. Assume quasi-steady laminar flow. 1
- 2. 5. Kerosine at 20o C is pumped at 0.15 m3 /s through 20 km of 16-cm-diameter cast-iron horizontal pipe. Compute the input power in kW required if the pumps are 85 percent efficient. 6. A small swimming pool is drained using a garden hose. The hose has 20 mm inside diameter, a roughness height of 0.2 mm, and is 30 m long. The free end of the hose is located 3 m below the elevation of the bottom of the pool. The average velocity at the hose discharge is 1.2 m/s. Estimate the depth of the water in the swimming pool. If the flow were inviscid, what would be the velocity? 7. Water flows at a rate of 0.04 m3 /s in a 0.12-m-diameter pipe that contains a sudden con- traction to a 0.06-m-diameter pipe. Determine the pressure drop across the contraction section. How much of this pressure difference is due to losses and how much is due to kinetic energy changes? 8. A straight 10-cm commercial-steel pipe is 1 km long and is laid on a constant slope of 5o . Water at 20o C flows downward, due to gravity only. Estimate the flow rate in m3 /h. What happens if the pipe length is 2 km? 9. A pump is located 4.5 m to one side of, and 3.5 m above a reservoir. The pump is designed for a flow rate of 6 lit/s. For satisfactory operation, the static pressure at the pump inlet must not be lower than 26 m of water gage. Determine the smallest standard commercial steel pipe that will give the required performance. 10. Water is pumped through a 60-m-long, 0.3-m-diameter pipe from a lower reservoir to a higher reservoir whose surface is 10 m above the lower one. The sum of the minor loss coefficients for the system is KL = 14.5. When the pump adds 40 kW to the water the flowrate is 0.2m3 /s. Determine the pipe roughness. 11. A large room uses a fan to draw in atmospheric air at 20o C through a 30-cm by 30-cm commercial-steel duct 12 m long, as shown in figure below. Estimate (a) the air flow rate in m3 /h if the room pressure is 10 Pa vacuum and (b) the room pressure if the flow rate is 1200 m3 /h. Neglect minor losses. 12. Heavy crude oil (SG = 50.925 and ν = 1.0 × 10−4 m2 /s) is pumped through a pipeline laid on flat ground. The line is made from steel pipe with 600 mm i.d. and has a wall thickness of 12 mm. The allowable tensile stress in the pipe wall is limited to 275 MPa by corrosion considerations. It is important to keep the oil under pressure to ensure that 2
- 3. gases remain in solution. The minimum recommended pressure is 500 kPa. The pipeline carries a flow of 6, 400 m3 per day. Determine the maximum spacing between pumping stations. Compute the power added to the oil at each pumping station. 13. The parallel galvanized-iron pipe system of figure below delivers gasoline at 20o C with a total flow rate of 0.036 m3 /s. If the pump is wide open and not running, with a loss coefficient KL = 1.5, determine (a) the flow rate in each pipe and (b) the overall pressure drop. 14. Water is pumped between two large open reservoirs through 1.5 km of smooth pipe. The water surfaces in the two reservoirs are at the same elevation. When the pump adds 20 kW to the water the flowrate is 1.0 m3 /s. If minor losses are negligible, determine the pipe diameter. 15. The three water-filled tanks shown in figure below are connected by pipes as indicated. If minor losses are neglected, determine the flowrate in each pipe. 3