Fluid Mechanics

An airstream of speed 160 m/s and temperature 3000 K travels on the inside of a 30 cm I.D. steel tube whose wall thickness is 2.5 mm. On the outside of the tube, water coolant flows coaxially in an annular space 6.1 mm thick. The coolant velocity is 10 m/s, and it has a local temperature of 15°C. Both flows are approximately fully developed. The pressure of the airstream is around 140 kPa. Estimate the maximum wall temperature of the tube.

1. What is the absolute pressure in mmHg at a depth of 10m of a lake if the barometric (aka the atmospheric) pressure is 1 atm?

2. The dead sea is a popular tourist destination. It is much easier to float due to the high salinity of the water. The specific gravity is 1.240. a. What is the density if water in the dead sea? b. What is the absolute water pressure on a diver at a depth of 500 feet in both atm and Pa?

3. Calculate the flow rate of your sink at home. a. What equation will you use? b. What will your measure? c. Calculate the flow rate in mL/min.

4. Your little brother leaves the faucet on every time he is brushing his teeth. You try to tell him to turn it off, but he says it's only on for a minute or two, so what's the difference? Assuming the sink faucet has a flow rate of 1 L/min and your little brother brushes his teeth twice a day, calculate the total amount of water he is wasting in gallons per year.

1) During laminar flow through a pipe, the volumetric flow rate Q is a function only of the tube radius R, the fluid viscosity u and the pressure drop per unit length dp/dx. Using the Buckingham T theorem, find an appropriate dimensionless relationship.

3) A fuel oil (μ-900 cp, SG=0.9) flows at 700 bbl/day through 1.5 in, schedule-40 pipe over a distance of 1500 ft. The discharge point is 30 ft above the inlet and the source, and the discharge are both at 1 atm (absolute). What is the horsepower required for a 70 % efficient pump? Neglect any minor losses. Note 1 bbl=1 barrel-5.61458 ft³.

6) Two open reservoirs are connected by three galvanized iron pipes in series: L1=300m,D1=200mm; L2=400m, D2=300mm; L3=1200m, D3=450 mm. If the flow is 400 m³/h of water (u=1 cP, p= 1000 kg/m³), determine the difference in elevation of the reservoirs. Neglect any minor friction losses. Use the Moody diagram to solve this problem.

4) An oil with a specific gravity of 0.833 and a viscosity of 3.3 cP is pumped from an open tank to a closed, pressurized tank maintained at 40 psig. The oil is pumped at a rate of 0.15 ft3/sec through 70 ft of 4-in, schedule-40 commercial steel pipe to the pump. The suction-side piping system contains a wide-open gate valve and a 90° elbow. On the discharge side of the pump, there is 300 ft of 3-in, schedule-40 commercial steel pipe. The discharge-side piping system contains two 90° elbows and a half-open globe valve, all after the pump. The liquid level in the open tank is 60 ft above the liquid level in the pressurized tank. The pump efficiency is 75%. Calculate the power required for the pump in hP.

5) A pipe system is composed of two horizontal coaxial commercial steel pipes. The diameter of the inner pipe is 33.4 mm, whereas the diameter of the outer pipe is 52.5 mm. This pipe system carries benzene and methanol (Pbenzene=881 kg/m³, benzene-6.51x10-4 Pa's and Pmethanol 788 kg/m³ Hmethanol-5.94x10-4 Pa*s at 20 degrees °C). Benzene flows through the space between the two pipes, whereas methanol flows through the inner pipe. The velocity <v> of both fluids is the same, v=2 m/s. The fluids also flow in the same direction. The inlet pressure is the same for both fluids. If, at some point, the inner pipe experiences a small crack, will the benzene enter the methanol stream or vice versa?