Fluid Mechanics Assignment - Finite Control Volume Analysis and Dimensional Analysis

Q1. The wind blows through a 7ft × 10ft garage door opening with a speed of 5 ft/s as shown in the figure. Determine the average speed, v, of the air through the two 3ft × 4ft openings in the windows.

Q2. Two rivers merge to form a larger river as shown in the figure below. At a location downstream from the junction (before the two streams completely merge), the non-uniform velocity profile is as shown and the depth is 6 ft. Determine the value of v.

Q3. At a sudden contraction in a pipe the diameter changes from D₁ to D₂. The pressure drop Δp, which develops across the contraction is a function of as well as the velocity, v, in the larger pipe, and the fluid density, ρ, and viscosity, μ. Use D₁, v, μ as repeating variables to determine a suitable set of dimensionless parameters. Why would it be incorrect to include the velocity in the smaller pipe as an additional variable?

Q4. It is desired to determine the wave height when wind blows across a lake. The wave height, H, is assumed to be a function of the wind speed, v, the water density ρ_w, the air density, ρ_a, the water depth, d, the distance from the shore, l, and the acceleration of gravity, g, as shown in the figure. Choose proper repeating variables to determine a suitable set of pi terms that could be used to describe this problem.