Applied Fluid Mechanics (7th Edition)
7th Edition
ISBN: 9780132558921
Author: Robert L. Mott, Joseph A. Untener
Publisher: PEARSON
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Chapter 1, Problem 1.45PP
One measure of a baseball pitcher's performance is earned run average or ERA. It is the average number of earned runs allowed if all the innings pitched were converted to equivalent nine-inning games Therefore, the units for ERA are runs per game,
1.45 Compute the pressure produced in the oil in a closed cylinder by a piston exerting a force of
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Problem 2 (55 pts). We now consider the FEM solution of Problem 1.(a) [5pts] Briefly describe the 4 steps necessary to obtain the approximate solution of thatBVP using the Galerkin FEM. Use the minimum amount of math necessary to supportyour explanations.(b) [20pts] Derive the weak form of the BVP.(c) [10pts] Assuming a mesh of two equal elements and linear shape functions, sketch byhand how you expect the FEM solution to look like. Also sketch the analytical solutionfor comparison. In your sketch, identify the nodal degrees of freedom that the FEMsolution seeks to find.(d) [10pts] By analogy with the elastic rod problem and heat conduction problem considered in class, write down the stiffness matrix and force vector for each of the twoelements considered in (c).(e) [10pts] Assemble the global system of equations, and verbally explain how to solve it.
An aluminum rod of length L = 1m has mass density ρ = 2700 kgm3 andYoung’s modulus E = 70GPa. The rod is fixed at both ends. The exactnatural eigenfrequencies of the rod are ωexactn =πnLqEρfor n=1,2,3,. . . .1. What is the minimum number of linear elements necessary todetermine the fundamental frequency ω1 of the system? Discretizethe rod in that many elements of equal length, assemble the globalsystem of equations KU = ω2MU, and find the fundamentalfrequency ω1. Compute the relative error e1 = (ω1 − ωexact1)/ωexact1.Sketch the fundamental mode of vibration.
Chapter 1 Solutions
Applied Fluid Mechanics (7th Edition)
Ch. 1 - 1.1 Convert 1250 millimeters to meters.Ch. 1 - Convert 1600 square millimeters to square metersCh. 1 - Convert 3.65x103 cubic millimeters to cubic metersCh. 1 - Convert 2.05 square meters to square millimetersCh. 1 - Convert 0.391 cubic meters to cubic millimetersCh. 1 - Convert 55.0 gallons to cubic metersCh. 1 - An automobile is moving at 80 kilometers per hour,...Ch. 1 - Convert a length of 25.3 feet to metersCh. 1 - Convert a distance of 1.36 miles to meters.Ch. 1 - Convert a length of 3.65 inches to millimeters.
Ch. 1 - Convert a distance of 2580 feet to meters.Ch. 1 - Convert a volume of 480 cubic feet to cubic...Ch. 1 - Convert a volume of 7390 cubic centimeters to...Ch. 1 - Convert a volume of 6.35 liters to cubic nneters.Ch. 1 - Convert 6.0 feet per second to meters per secondCh. 1 - Convert 2500 cubic feet per minute to cubic meters...Ch. 1 - A car travels 0.50 km in 10.6 s. Calculate its...Ch. 1 - In an attempt at a land speed record, a car...Ch. 1 - A car travels 1000 ft in 14 s. Calculate its...Ch. 1 - In an attempt at a land speed record, a car...Ch. 1 - A body starting from rest with constant...Ch. 1 - A body starting from rest with constant...Ch. 1 - A body starting from rest with constant...Ch. 1 - A body starting from rest with constant...Ch. 1 - The formula for kinetic energy is KE=mv2, where m...Ch. 1 - The formula for kinetic energy is KE=12mv2, where...Ch. 1 - The formula for kinetic energy is KE=12mv2, where...Ch. 1 - The formula for kinetic energy is KE=12mv2, where...Ch. 1 - The formula for kinetic energy is KE=12mv2, where...Ch. 1 - The formula for kinetic energy is KE=12mv2 where m...Ch. 1 - The formula for kinetic energy is KE=12mv2, where...Ch. 1 - The formula for kinetic energy is KE=12mv2, where...Ch. 1 - The formula for kinetic energy is KE=12mv2, where...Ch. 1 - The formula for kinetic energy is KE=12mv2, where...Ch. 1 - The formula for kinetic energy is KE=12mv2, where...Ch. 1 - The formula for kinetic energy is where m = mass...Ch. 1 - The formula for kinetic energy is KE=12mv2, where...Ch. 1 - The formula for kinetic energy is KE=12mv2, where...Ch. 1 - One measure of a baseball pitcher's performance is...Ch. 1 - One measure of a baseball pitcher's performance is...Ch. 1 - One measure of a baseball pitcher's performance is...Ch. 1 - One measure of a baseball pitcher's performance is...Ch. 1 - One measure of a baseball pitcher's performance is...Ch. 1 - One measure of a baseball pitcher's performance is...Ch. 1 - One measure of a baseball pitcher's performance is...Ch. 1 - One measure of a baseball pitcher's performance is...Ch. 1 - One measure of a baseball pitcher's performance is...Ch. 1 - One measure of a baseball pitcher's performance is...Ch. 1 - One measure of a baseball pitcher's performance is...Ch. 1 - One measure of a baseball pitcher's performance is...Ch. 1 - One measure of a baseball pitcher's performance is...Ch. 1 - One measure of a baseball pitcher's performance is...Ch. 1 - One measure of a baseball pitcher's performance is...Ch. 1 - One measure of a baseball pitcher's performance is...Ch. 1 - One measure of a baseball pitcher's performance is...Ch. 1 - One measure of a baseball pitcher's performance is...Ch. 1 - Compute the pressure change required to cause a...Ch. 1 - Compute the pressure change required to cause a...Ch. 1 - Compute the pressure change required to cause a...Ch. 1 - For the conditions described in Problem 1.59...Ch. 1 - A certain hydraulic system operates at 3000 psi....Ch. 1 - A certain hydraulic system operates at 20.0 MPa....Ch. 1 - A measure of the stiffness of a linear actuator...Ch. 1 - 1.64 Repeat Problem 1.63 but change the length of...Ch. 1 - Repeat Problem 1.6319 but change the cylinder...Ch. 1 - Using the results of Problems 1.63-1.65, generate...Ch. 1 - Calculate the mass of a can of oil if it weighs...Ch. 1 - Calculate the mass of a tank of gasoline if it...Ch. 1 - '1.69 Calculate the weight of 1m3 of kerosene if...Ch. 1 - Calculate the weight of a jar of castor oil if it...Ch. 1 - Calculate the mass of 1 gal of oil if it weighs...Ch. 1 - Calculate the mass of 1ft3 of gasoline if it...Ch. 1 - Calculate the weight of 1ft3 of kerosene if it has...Ch. 1 - Calculate the weight of 1 gal of water if it has a...Ch. 1 - Assume that a man weighs 160 lb (force) Compute...Ch. 1 - In the United States, hamburger and other meats...Ch. 1 - The metric ton is 1000 kg (mass). Compute the...Ch. 1 - Convert the force found in Problem 1.77 to lb.Ch. 1 - Determine your weight in lb and N and your mass in...Ch. 1 - The specific gravity of benzene is 0.876....Ch. 1 - Air at 16 C and standard atmospheric pressure has...Ch. 1 - Carbon dioxide has a density of 1.964kg/m3 at 0 C....Ch. 1 - A certain medium lubricating oil has a specific...Ch. 1 - At 100 C mercury has a specific weight of...Ch. 1 - A cylindrical can 150 mm in diameter is filled to...Ch. 1 - Glycerin has a specific gravity of 1.258. How much...Ch. 1 - The fuel tank of an automobile holds 0.095m3. If...Ch. 1 - The density of muriatic acid is 1200 kg / m3...Ch. 1 - Liquid ammonia has a specific gravity of 0.826....Ch. 1 - Vinegar has a density of 1080 kg / m3 Calculate...Ch. 1 - Methyl alcohol has a specific gravity of 0.789....Ch. 1 - A cylindrical container is 150 mm in diameter and...Ch. 1 - A storage vessel for gasoline ( sg=0.68 ) is a...Ch. 1 - What volume of mercury (sg = 13.54) would weigh...Ch. 1 - A rock has a specific gravity of 2.32 and a volume...Ch. 1 - The specific gravity of benzene is 0.876....Ch. 1 - Air at 59 F and standard atmospheric pressure has...Ch. 1 - Carbon dioxide has a density of 0.003 81 slug/ft3...Ch. 1 - A certain medium lubricating oil has a specific...Ch. 1 - At 212F mercury has a specific weight of 834...Ch. 1 - One gallon of a certain fuel oil weighs 7.50 lb....Ch. 1 - Glycerin has a specific gravity of 1.258. How much...Ch. 1 - The fuel tank of an automobile holds 25.0 gal. If...Ch. 1 - The density of muriatic acid is 1.20 g/cm3....Ch. 1 - Liquid ammonia has a specific gravity of 0.826....Ch. 1 - Vinegar has a density of 1.08 g/cm3. Calculate its...Ch. 1 - Alcohol has a specific gravity of 0.79. Calculate...Ch. 1 - A cylindrical container has a 6.0-in diameter and...Ch. 1 - A storage vessel for gasoline (sg = 0.68) is a...Ch. 1 - How many gallons of mercury (sg = 13.54) would...Ch. 1 - A rock has a specific gravity of 2.32 and a volume...Ch. 1 - A village of 75 people desires a tank to store a...Ch. 1 - A cylindrical tank has a diameter of 38 in with...Ch. 1 - What is the required rate, in N/min, to empty a...Ch. 1 - An empty tank measuring 1.5 m by 2.5 m on the...Ch. 1 - A tank that is 2 ft in diameter and 18 in tall is...Ch. 1 - A standard pump design can be upgraded to higher...Ch. 1 - What is the annual cost to run a 2 HP system if it...Ch. 1 - Determine the displacement, in liters, for one...Ch. 1 - Determine the flow rate, in m3/hr, for another...Ch. 1 - At what speed, in rpm, does a single cylinder pump...Ch. 1 - Prob. 2CAEA
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- Problem 1 (65 pts, suggested time 50 mins). An elastic string of constant line tension1T is pinned at x = 0 and x = L. A constant distributed vertical force per unit length p(with units N/m) is applied to the string. Under this force, the string deflects by an amountv(x) from its undeformed (horizontal) state, as shown in the figure below.The PDE describing mechanical equilibrium for the string isddx Tdvdx− p = 0 . (1)(a) [5pts] Identify the BCs for the string and identify their type (essential/natural). Writedown the strong-form BVP for the string, including PDE and BCs.(b) [10pts] Find the analytical solution of the BVP in (a). Compute the exact deflectionof the midpoint v(L/2).(c) [15pts] Derive the weak-form BVP.(d) [5pts] What is the minimum number of linear elements necessary to compute the deflection of the midpoint?(e) [15pts] Write down the element stiffness matrix and the element force vector for eachelement.arrow_forwardProblem 1 (35 pts). An elastic string of constant line tension1 T is pinned at x = 0 andx = L. A constant distributed vertical force per unit length p (with units N/m) is appliedto the string. Under this force, the string deflects by an amount v(x) from its undeformed(horizontal) state, as shown in the figure below.Force equilibrium in the string requires thatdfdx − p = 0 , (1)where f(x) is the internal vertical force in the string, which is given byf = Tdvdx . (2)(a) [10pts] Write down the BVP (strong form) that the string deflection v(x) must satisfy.(b) [2pts] What order is the governing PDE in the BVP of (a)?(c) [3pts] Identify the type (essential/natural) of each boundary condition in (a).(d) [20pts] Find the analytical solution of the BVP in (a).arrow_forwardProblem 2 (25 pts, (suggested time 15 mins). An elastic string of line tension T andmass per unit length µ is pinned at x = 0 and x = L. The string is free to vibrate, and itsfirst vibration mode is shown below.In order to find the frequency of the first mode (or fundamental frequency), the string isdiscretized into a certain number of linear elements. The stiffness and mass matrices of thei-th element are, respectivelyESMi =TLi1 −1−1 1 EMMi =Liµ62 11 2 . (2)(a) [5pts] What is the minimum number of linear elements necessary to compute the fundamental frequency of the vibrating string?(b) [20pts] Assemble the global eigenvalue problem and find the fundamental frequency ofvibration of the stringarrow_forward
- I need part all parts please in detail (including f)arrow_forwardProblem 3 (10 pts, suggested time 5 mins). In class we considered the mutiphysics problem of thermal stresses in a rod. When using linear shape functions, we found that the stress in the rod is affected by unphysical oscillations like in the following plot E*(ux-a*T) 35000 30000 25000 20000 15000 10000 5000 -5000 -10000 0 Line Graph: E*(ux-a*T) MULT 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Arc length (a) [10pts] What is the origin of this issue and how can we fix it?arrow_forwardanswer the questions and explain all of it in words. Ignore where it says screencast and in class explanationarrow_forward
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