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) = 10 ^{ 6 } , k(kilo) = 10 ^{ 3 } , 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/s ^{ 2 } = 32.2 ft/s ^{ 2 }
- 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/m ^{ 3 } , g _{ w } = 9810 N/m ^{ 3 }
- B.G. (or E.S.), g _{ w } = 62.4 lb/ft ^{ 3 }
- bulk modulus of elasticity for liquids: E = - D p/( D V/V) or E = - D p/( D v/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:
- p _{ 2 } -p _{ 1 } = - g (z _{ 2 } -z _{ 1 } )
- 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
Copyright 2008,
by the Contributing Authors.
Cite/attribute Resource
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admin. (2006, April 17). Lecture 9. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Civil_and_Environmental_Engineering/Fluid_Mechanics/lect9.htm.
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