Mechanical Engineering: Fundamentals of Fluid Flow exam

(Fall 2018) ME721 Fundamentals of Fluid Flow

Homework Assignment #1 (Due date: 09/27/2018)

(*) Please include all the intermediate steps.

1. (20 points) A spar buoy is a buoyant rod weighted to float and

protrude vertically as shown below. Suppose that the buoy is maple

wood (SG = 0.6), 2 in by 2 in by 12 ft, floating in seawater (SG =

1.025). How many pounds of steel (SG = 7.85) should be added to

the bottom end so that h = 18 in? The specific weight of water is 62.4

lbf/ft3. Note that when you add steel, you do not only increase the

weight of the buoy, but also increase the buoyant force (by the

amount of added volume).

2. (20 points) A flat plate is hinged at Point O to a horizontal surface. The hinged plate is slowly

rotated toward the horizontal surface at a constant clockwise angular velocity  squeezing out the

liquid between the two plates. Calculate the velocity u(x) as a function of  and . Use the mass

conservation equation expressed in the second integral form.

3. (20 points) A rocket is rising at the speed of 𝑉(𝑡) while burning propellant at the mass consumption

rate of �̇�𝑟. The hot jet of gases, the product of combustion, escapes through the nozzle at the very

high speed of 𝑣𝑒 with respect to the rocket. If the mass of the rocket was 𝑀0 when it was rising at the speed of 𝑉0, find 𝑉(𝑡) as a function of the other variables.