MIDTERM EXAMINATIONMEM 220: BASIC FLUID MECHANICS February 1, 2007 NAME _____________________________________ Multiple Choice: Solve: Problem 1 Problem 2 Problem 3 ____________ points of 10 ____________ ____________ ____________ points of 30 points of 30 points of 30 TOTAL ____________ points of 100 Please remember to: 1. Be careful with your units 2. Show all work and explain steps you take 3. List all assumptions 4. Write neatly 5. Only exams in non-erasable ink will be eligible for re-grade Multiple Choice: select all that apply 1. What is a fluid? A. Liquid or gas B. Substance that deforms under any shearing stress C. Substance that cannot be compressed D. Substance with large cohesive forces 2. Fluids for which the shear stress is linearly related to the rate of shear strain are called: A. viscous fluids B. Newtonian fluids C. non-Newtonian fluids D. Bingham plastics 3. What two types of forces act on a fluid element? A. Gravitational and body forces B. Shearing and surface forces C. Body and surface forces D. Pressure and surface forces 4. When a surface is submerged in a fluid, the resultant pressure force on the body acts in which direction? A. In the same direction as gravity. B. Perpendicular to the surface of the body. C. Tangent to the surface of the body. D. Normal to the free surface of the fluid. 5. The pressure in a fluid A. Rises with depth B. Decreases with depth C. Changes laterally D. Is constant laterally 6. Write an expression or definition for: A. Static pressure: B. Dynamic pressure: C. Stagnation pressure: D. Total pressure: 7. What is the pressure at a center of a tornado if the pressure outside the tornado is atmospheric? A. P(center) is greater than P(outside) B. P(center) is less than P(outside) C. P(center) is equal to P(outside) D. P(center) is a negative gage pressure 8. The form of the Bernoulli equation (P + ½ rhoV2 + rhogz) applies for: A. Inviscid flow B. Viscous flow C. Incompressible flow D. Compressible flow E. Steady flow 9. For cavitation to occur: A. The fluid temperature must be increased B. The fluid pressure must fall below the vapor pressure C. The fluid pressure must rise above the vapor pressure D. The fluid must be taken to a higher altitude. 10. For a body partially submerged in a fluid and at equilibrium, which of the following is a true statement? A. The weight of the body is equal to the weight of the volume of fluid displaced B. The weight of the body is less than the weight of the volume of fluid displaced C. The weight of the body is greater than the weight of the volume of fluid displaced D. The specific gravity of the body is greater than the specific gravity of the fluid Solve. 1. Your garden hose is too short to reach the garden. For DH = 0.625 inches and DN = 0.375 inches, A. What is the nozzle exit velocity, in terms of the gage pressure inside the hose? B. What is the velocity inside the hose, in terms of the gage pressure inside the hose? C. What is the minimum gage pressure required inside the hose for the water to reach the garden which is 125 ft away? D. Your hose can’t generate enough pressure to reach the garden. You rig a rope system to slide a water bucket to the garden. How fast can you accelerate a 1 ft diameter bucket without spilling any water, if the water level is 1 inch below the top of the bucket? Patm DN DH Pin 45° 125 ft Garden 2. Global Warming. You are a marine biologist, concerned about how global warming may affect delicate creatures at the bottom of the ocean. You create a large test tank and use a U-tube manometer to measure pressure differences in the bottom of the tank. A. Given h1=50 cm, h2=250 cm, and h3=75 cm what is the height of the seawater in the tank? B. You add 960 m3 of seawater to the tank, which has a diameter of 3.5 m. How much would the height of the mercury in the manometer change? C. If you added tap water instead of seawater, would the change in mercury height be more or less? Explain. D. If global warming heats up the atmosphere by 10 °C, how would the pressure at sea level change? Assume the atmosphere is an ideal gas up to 10 km, and the pressure at 10 km is 26,500 Pa. hw Mercury Seawater h3 h1 h2 3. You have the submerged gate shown in the diagram, which is marked with 2 buoys so that passing ships will not hit the gate. The top buoy is only halfway submerged. The diameter of each buoy is 100 cm, and they are made of a material of density ρb=100 kg/m3. The height of the seawater is 10 m, the radius of the gate is 1 m, and the width of the gate is 5 m. A. What is the tension in the buoy rope? B. What are the horizontal and vertical forces on the curved section of the gate? C. What torque is needed to keep the gate closed? hw Rg Hinge Ocean floor Equation Sheet for Midterm 1 1. ˆ ˆ − ∇ P − ρ gk = ρ a 15. ∂p ρV 2 − = ∂n ℜ 2. ∇P = ∂p ˆ ∂p ˆ ∂p ˆ i+ j+ k ∂x ∂y ∂z 16. τ =μ du dy 3. 4. 5. 6. 7. − ∂p = ρg ∂z 17. g = 9.81 m/s2 = 32.2 ft/s2 18. Patm = 14.7 psi = 101300 Pa p 2 − p1 = ρgh p = ρRT FR = ρghc A yR = I xc + yc yc A 8. 9. FB = ρg∀ ay ∂z =− ∂y g + az 10. ∂z rω 2 = ∂r g 11. ∫ dp 1 + V 2 + gz = C o ρ 2 12. ∫ρ P+ dp +∫ V2 dn + gz = C o ℜ 13. 1 ρV 2 + ρgz = C o 2 14. P + ρ∫ V2 dn + ρgz = C o ℜ