Lecture 9

CEE 3500 TEST 1 INFORMATION

• The first test took place on Monday, February 6, 2006
• Download the test solution here (pdf file)
• Students were allowed to have the following:
• Reference sheet(s) with formulas and other notes were allowed - The exam is closed book
• Pens and/or pencils, erasers, rulers, etc.
• A calculator
• Partial credit was given in grading each problem.

Subjects

• The test included four problems addressing the following subjects:
• Unit conversions - Some useful conversions:
• 1 m = 3.28 ft, 1 ft = 0.3048 m = 12 inches
• 1 kg = 0.0685 slugs, 1 slug = 14.59 kg
• 1 lb = 4.448 N, 1 N = 0.2248 lb
• 1 psi = 144 psf
• S.I. prefixes: M (mega) = 10⁶, k(kilo) = 10³, m(milli) = 10^-3
• Fluid properties:
• density: r = m/V, m = mass, V = volume, W = weight, g = acceleration of gravity
• specific volume: v = 1/r = V/m
• specific weight: g = W/V = r g, with g = 9.81 m/s² = 32.2 ft/s²
• specific gravity: s = r/r_w, s = g/g_w, subindex w indicates density or specific weigth of water
• typical values for water:
• S.I., r_w = 1000 kg/m³, g_w = 9810 N/m³
• B.G. (or E.S.), g_w = 62.4 lb/ft³
• bulk modulus of elasticity for liquids: E = -Dp/(DV/V) or E = -Dp/(Dv/v) , p = pressure, V = volume, v = specific volume
• viscosity
• Newton's of viscosity: t = m (dv/dy), m = dynamic or absolute viscosity
• for small gaps assume linear velocity distribution: t = m (V/Y), V = velocity of moving wall, Y = gap size
• kinematic viscosity: n = m/r
• surface tension
• s = force/length
• see equation for capillary rise in tubes
• vapor pressure (p_v) - related to cavitation in liquids
• Fluid statics:
• Absolute and gage pressures
• p_gage = 0 in free-surface open to the atmosphere
• p_abs = p_gage + p_atm
• Pressure variation in fluids: dp/dz = -g, z = vertical coordinate (positive upwards), g = specific weight
• Pressure variation in liquids:
• p₂-p₁ = -g(z₂-z₁)
• p = g h, gage pressure if free-surface open to the atmosphere, h = depth measured from free surface
• Manometer problems
• follow rules for writing manometric equations:
• Write pressure at starting point
• Add g h if moving downwards to next meniscus
• Subtract g h if moving upwards to next meniscus
• Make sum equal to pressure at ending point
• remember to take into account the specific gravity of the different fluids involved
• typically in a gas enclosure the pressure is constant
• Forces on plane areas including calculation of moments, friction forces, etc.
• Pressure forces act NORMAL to an area, always
• Force = volume of pressure prism
• Location of forces due to rectangular (half-way) and triangular (1/3 from the base) pressure distributions
• Force = (pressure at centroid)x(area)
• y_p = y_c + I_c/(y_c*A), location of center of pressure on an inclined or vertical area, origin of y coincides with the free surface-inclined plane intersection
• Use of equivalent moment to find arm of resultant force to locate center of pressure
• Forces on curved areas
• Horizontal force = same as that on a vertical projection of the curved surface
• Vertical force = weight of the liquid ABOVE the curved surface (plus any gas pressure overload in the free surface)
• Buoyancy force analysis
• Bouyancy force = weight of fluid displaced by submerged or floating body, acts vertically upwards always
• Liquids in accelerating containers

How prepare for the test

• Read the sections in the book for each lecture as indicated in the class schedule
• Download references provided for each lecture (follow the links in the class schedule) and study the examples given in those references (e.g., worked examples, lecture notes -- ignore the additional materials for each lecture)
• Download additional examples provided by the instructor -- these are available in the class notes web page -- study the solved problems, try the proposed problems
• Download assignment solutions from the Assignments web page, study those solutions
• Check out sample tests from Dr. Rahmeyer's web page (he was the CEE3500 instructor for the last few years)
• Download and try the following sample tests:
• Sample Test 1 (PDF) - Download solution to sample test 1 (PDF)
• Sample Test 2 (PDF) - Download solution to sample test 2 (PDF)
• Sample Test 3 (PDF) - Download solution to sample test 3 (PDF)
• In Problem 3, the liquid is water
• In Problem 4, assume the width of the dam is 1 ft (i.e., calculate the forces per unit length of dam)
• Sample Test 4 (PDF) - Download solution to sample test 4 (PDF)
• In problem 2, there is air above the free surface at A
• Sample Test 5 (PDF) - Download solution to sample test 5 (PDF)
• Fall 2005 First Test (PDF) - Download solution to Fall 2005 First Test (PDF)
• Practice, practice, practice