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# 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

Copyright 2008, by the Contributing Authors. Cite/attribute Resource . 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. This work is licensed under a Creative Commons License