ENSC 3233 - Homework 7: Fluid Dynamics Problems - Prof. Glenn Brown, Assignments of Fluid Mechanics

Download ENSC 3233 - Homework 7: Fluid Dynamics Problems - Prof. Glenn Brown and more Assignments Fluid Mechanics in PDF only on Docsity! ENSC 3233 Chapter 7 Homework Due: 2/25/2009 1. An airplane with a wing cord of 3.50 m flies at 300 km/h at an air temperature of 15 C and pressure of 101.3 kPa. A 1:20 scale model is tested in a wind tunnel. The velocity (V), cord length (C), and kinematic viscosity (ν) are known to be the relevant variables. a) At what velocity should the wind tunnel run if the air is the same temperature and pressure? b) What velocity would be needed if the model is run in a water flume? 2. A 1:100 scale model of a dam spillway is used to predict the performance of the prototype. Assume that similarity with gravity and inertia are maintained. At one flow in the model the depth of flow on the spillway was 0.0250 m and the flow rate was 0.0150 m3/s. What will be the corresponding depth of flow and discharge in the prototype? 3. A 1:50 scale model of a ship is towed at 5.00 km/hr with a force of 10.00 N. Assuming the same seawater in the towing basin and the ocean, what will be the corresponding speed and force if you assume: a) similarity is maintained for density and gravity. b) similarity is maintained for density and surface tension. c) similarity is maintained for density and viscosity. 4. Use dimensional analysis to find an expression for the local velocity, u in a smooth pipe if the local velocity depends on the mean velocity, V, the diameter, D, the distance from the wall, y, the density, ρ, and the absolute viscosity, µ. Use mass as a fundamental unit and choose repeating variables in the order; V, D, ρ, u, y, µ. 5. Drag force exerted on a sphere in a fluid is a function of the diameter, D, velocity, V, viscosity, µ, and density, ρ. The data plot (Figure P5) shows results from tests on a sphere (d = 4”) in a water tunnel. If µ = 2.3 x 10 -5 lb*s/ft2, and ρ = 1.94 slugs/ft3, what is the drag on a balloon (d = 8 ft) with a velocity of 3 ft/s in air? Assume µair = 3.7 x 10 -7 lb*s/ft2 and ρair = 2.38 x 10 -3 slugs/ft3. Choose repeating variables in the order; D, V, ρ, µ.