Fluid Mechanics

Fuel flows in a 3.5-m pipe from a fuel tank to the pump of a jet engine. The flow rate is 200 1/min. At high altitudes the fuel-tank pressure is low, and there may be considerable danger of the fuel "boiling" or cavitating as it enters the pump. In such a case the pump would be vapor locked and would cease to deliver fuel to the engine. Show qualitatively how the pressure drop in the line varies with its diameter (over a wide range). What would the mini- mum pipe diameter be if a pipe pressure loss of only 3 kPa were tolerable? The pipe has no sharp bends or elbows.

Consider uniform flow past a cylinder with a V-shaped wake as shown. Pressure at (1) equals pressure at (2). Let b equal the width into the paper. (a) Develop a formula for the force F on the cylinder. (b) Also compute the drag coefficient C₁ = F/(pU²Lb).

Objective: - To evaluate: For a variety of flow rates, find the pressure losses through valves, along pipes, and across fittings. • To derive K values from a real experiment for fittings and valves. • To compare the actual friction factor with that predicted by the Moody chart.

Consider an incompressible fluid above an infinite plate located in the ₁-3 plane (at x2 = 0), in the absence of body forces. The plate oscillates sinusoidally along with a velocity amplitude to and angular frequency w. The velocity of the liquid is given by and is the kinematic viscosity (related to the dynamic viscosity and density p according to v = µ/p). (a) Verify that the given fluid velocity satisfies the axiom of mass balance. (b) Evaluate grad v and its symmetric part D. (c) Evaluate curl v. (d) Evaluate the acceleration a of the fluid. (e) For an incompressible Newtonian fluid the stress tensor is given by T = -pI+2μD, where I is the identity tensor. For the given velocity and pressure, evaluate the stress T. (f) Verify that your solution for T satisfies the axiom of linear momentum balance. (g) Evaluate the traction vector on the oscillating plate. (h) What are the eigenvalues and eigenvectors of D? Hint: Simplify the notation by using D₁, for the non-zero components of D instead of the full expressions evaluated in part (b). (i) What is the relation between the eigenvalues and eigenvectors of D and T?

1. objectives - compare the workings and characteristics of the three most common types of flow meters (variable area, orifice plate, and venturi). - find out how precise each meter is and how much energy it loses

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?

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.

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.

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.

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.