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AE 201 Embry-Riddle Aeronautical University Engineering Worksheet

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AE 201 – Spring 2022 Problem Set 4 1. (10 pts) During measurements in the ERAU wind tunnel, the pressure and temperature of the air in SI units are found to be 102.3 kPa and 15.7◦ C, respectively. Calculate the density of the air in the tunnel. Repeat the problem of finding the density of the air if the pressure is measured in USC units as 14.61 pounds per square inch (psi) at a temperature of 71.1◦ F. 2. (10 pts) A well-type water manometer has a long tube inclined at an angle of 30 degrees from the horizontal, as shown in the figure below. The reading on the scale between the fluid at the top of the well and the top of the fluid in the tube is 4.82 cm. What will be the value of ∆H? If the density of water is assumed to be 1,000 kg m−3 , what is the difference between the applied pressure and the reference pressure? 3. (10 pts) Explain the principle of buoyancy. Consider a solid rectangular body of dimensions ∆x, ∆y and ∆z that is completely immersed in a fluid of constant density. By considering the pressure forces on the body then show that the upforce on the body is equal to the weight of the fluid that is displaced by the body, i.e., Archimedes’ principle. 4. (10 pts) Why does the viscosity of a gas generally decrease with decreasing temperature whereas for a liquid its viscosity generally increases? Calculate and plot using Matlab the variation in the coefficient of dynamic viscosity of air in USC units from 35◦ F to 120◦ F. Sutherland’s Law can be expressed as 1.5 T T0 + S µ = µ0 T0 T +S where T0 = 518.7◦ R, S = 198.72◦ R and µ0 = 3.63 × 10−7 slugs s−1 ft−1 . Note: Be sure to attach a copy of your Matlab code and the graph to your homework submission (export the graph from MatLab). 5. (10 pts) Consider a water-filled container with a hinged cover gate, as shown in the figure below. The length of the steel gate is 1 m, its width (into the paper) is 0.5 m, and it has a mass of 400 kg. The density of the water in the container is 1,000 kg/m3 . First, find the pressure acting on the gate in terms of h1 and h2 and draw a free-body diagram of the forces and moments acting on the gate. The determine the water level h1 required to force open the gate. Finally, if a 200 kg mass is then placed at 0.8 m from the hinge to hold the gate closed with this water level, what will be the new water level h1 to force open the gate? 6.
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