Applied Fluid Mechanics (7th Edition)
7th Edition
ISBN: 9780132558921
Author: Robert L. Mott, Joseph A. Untener
Publisher: PEARSON
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Chapter 6, Problem 6.46PP
Repeat Problem 6.45, except specify suitable sizes for the suction lines to maintain the velocity between 2.0 ft/s and 7.0 ft/s for 30 gal/min of flow.
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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.
Chapter 6 Solutions
Applied Fluid Mechanics (7th Edition)
Ch. 6 - Convert a volume flow rate of 3.0 gal/min to...Ch. 6 - Convert 459 gal/min to rrP/s.Ch. 6 - Convert 3720 gal/min to mJ/sCh. 6 - Convert 34.3 gal/min to mJ/sCh. 6 - Convert a volume flow rate of 125 L/min to m3/s.Ch. 6 - Convert 4500 L/min to m5/s.Ch. 6 - Convert 15 000 L/minto m3/s.Ch. 6 - Convert 459 gal/min to L/mninCh. 6 - Convert 3720 gal/min to L/minCh. 6 - Convert 23.5cm2/stom3/s.
Ch. 6 - '6.11 Convert 0.296cm5/stom3/s.Ch. 6 - Convert 0.105 cm3/s to L/minCh. 6 - Convert 3.53103m3/s to L/min.Ch. 6 - Convert 5.26106m3stoL/min.Ch. 6 - Prob. 6.15PPCh. 6 - Convert 20 gal/min to ft'/s.Ch. 6 - Convert 2500 gal/min to ft5/s.Ch. 6 - Convert 2.50 gal/min to ft3/s.Ch. 6 - Convert 125 ft3/s to gal/minCh. 6 - Convert 0.060 ft3/s to gal/min.Ch. 6 - Convert 0.03 ft5/s to gal/minCh. 6 - Convert ft5/s sto gal/minCh. 6 - Table 6.21 lists the range of typical volume flow...Ch. 6 - Table 6.2 lists the range of typical volume flow...Ch. 6 - A certain deep-well pump for a residence is rated...Ch. 6 - A small pump delivers 0.85 gal/h of liquid...Ch. 6 - A small metering pump delivers 11.4 gal of a water...Ch. 6 - A small metering pump delivers 19.5 mL/min of...Ch. 6 - Water at 10 C is flowing at 0.075 m3/s Calculate...Ch. 6 - Oil for a hydraulic system (sg =0.90 ) is flowing...Ch. 6 - A liquid refrigerant (sg = 1.08) is flowing at a...Ch. 6 - After the refrigerant from Problem 6.31 flashes...Ch. 6 - A fan delivers 640ft3/min (CFM) of air. If the...Ch. 6 - A large blower for a furnace delivers 47000ft3/min...Ch. 6 - A furnace requires 1200 Ib/h of air for efficient...Ch. 6 - If a pump removes 1.65 gal/min of water from a...Ch. 6 - Calculate the diameter of a pipe that would carry...Ch. 6 - If the velocity of a liquid is 1.65 ft/s in a...Ch. 6 - When 2000 L/min of water flows through a circular...Ch. 6 - Water flows at 1.20 m/s in a circular section with...Ch. 6 - Figure 6.16 shows a fabricated assembly made from...Ch. 6 - A standard Schedule 40 steel pipe is to be...Ch. 6 - If water at 180 F is flowing with a velocity of...Ch. 6 - A standard steel tube, 1.5 25-mm OD 3 1,5-mm wall...Ch. 6 - The recommended velocity of flow in the discharge...Ch. 6 - Repeat Problem 6.45, except specify suitable sizes...Ch. 6 - Table 6.2 shows the typical volume flow rate for...Ch. 6 - Repeat Problem 6.47 but use Schedule 80 DM pipeCh. 6 - Compute the resulting velocity of flow if 400...Ch. 6 - Repeat Problem 6.49 for a DN 50 Schedule 30 pipe.Ch. 6 - Compute the resulting velocity of flow if 400...Ch. 6 - Repeat Problem 6.51 for a 4-in Schedule 30 pipe.Ch. 6 - From the list of standard hydraulic steel tubing...Ch. 6 - A standard 6-in Schedule 40 steel pipe is carrying...Ch. 6 - For Problems 6.55-6.57, use Fig. 6.3 O to specify...Ch. 6 - For Problems 6.55-6.57, use Fig. 6.3 to specify...Ch. 6 - For Problems 6.55-6.57, use Fig. 6.3 O to specify...Ch. 6 - A venturi meter is a device that uses a...Ch. 6 - A flow nozzle, shown in Fig. 6.18 is used to...Ch. 6 - Gasoline (sg = 0.67) is flowing at 0.11 m3/s in...Ch. 6 - Water at 10 C is flowing from point A to point B...Ch. 6 - Calculate the volume flow rate of water at 5 C...Ch. 6 - Calculate the pressure required in the larger...Ch. 6 - Kerosene with a specific weight of 50.0 lb/ft3 is...Ch. 6 - For the system shown in Fig. 6.23 ; calculate (a)...Ch. 6 - For the system shown in Fig. 6.24ss, calculate (a)...Ch. 6 - For the tank shown in Fig. 6.25lO, calculate the...Ch. 6 - Calculate the pressure of the air in the sealed...Ch. 6 - For the siphon in Fig. 6.26, calculate (a) the...Ch. 6 - For the siphon in Fig. 6.26 , calculate the...Ch. 6 - For the siphon in Fig. 6.26 , assume that the...Ch. 6 - For the siphon shown in Fig. 6.27, calculate (a)...Ch. 6 - For the special fabricated reducer shown in Fig....Ch. 6 - In the fabricated enlargement shown in Fig. 6.29,...Ch. 6 - Figure 6.30 shows a manometer being used to...Ch. 6 - For the venturi meter shown in Fig. 6.30,...Ch. 6 - Oil with a specific weight of 8.64 kN/m3 flows...Ch. 6 - The venturi meter shown in Fig. 6.32 iP carries...Ch. 6 - Oil with a specific gravity of 0.90 is flowing...Ch. 6 - Oil with a specific gravity of 0.90 is flowing...Ch. 6 - Gasoline (sg = 0.67) is flowing at 4.0 ft3/s in...Ch. 6 - Oil with a specific weight of 55.0lb/ft3 flows...Ch. 6 - Draw a plot of elevation head, pressure head,...Ch. 6 - Prob. 6.84PPCh. 6 - Figure 6.36 shows a system in which water flows...Ch. 6 - Figure 6.37 shows a venturi meter with a U-tube...Ch. 6 - For the tank shown in Fig. 6.38, compute the...Ch. 6 - What depth of fluid above the outlet nozzle is...Ch. 6 - Derive Torricelli's theorem for the velocity of...Ch. 6 - Solve Problem 6.88 using the direct application of...Ch. 6 - To what height will the jet of fluid rise for the...Ch. 6 - To what height will the jet of water rise for the...Ch. 6 - What pressure is required above the water in Fig....Ch. 6 - What pressure is required above the water in Fig....Ch. 6 - Compute the time required to empty the tank shown...Ch. 6 - Compute the time required to empty the tank shown...Ch. 6 - Compute the time required to empty the tank shown...Ch. 6 - Compute the time required to empty the tank shown...Ch. 6 - Compute the time required to reduce the depth in...Ch. 6 - Compute the time required to reduce the depth in...Ch. 6 - Compute the time required to reduce the depth in...Ch. 6 - Compute the time required to reduce the depth in...Ch. 6 - Prob. 6.103PPCh. 6 - Repeat Problem 6.101 if the tank is sealed and a...Ch. 6 - Repeat Problem 6.96 if the tank is sealed and a...Ch. 6 - Repeat Problem 6.100 if the tank is sealed and a...Ch. 6 - A village currently carries water by hand from a...Ch. 6 - A "spa tub" is to be designed to replace bath tubs...Ch. 6 - A simple soft drink system relies on pressurized...Ch. 6 - A concept team for a toy company is considering a...Ch. 6 - 6.111 Bernoulli's principle applies to Venturi...Ch. 6 - Prob. 6.112PPCh. 6 - You are to develop a mixing valve for use in a...Ch. 6 - Prob. 6.114PPCh. 6 - You would like to empty the in-ground pool in the...Ch. 6 - Prob. 6.116PPCh. 6 - Create a spreadsheet for computing the values of...Ch. 6 - Prob. 2APCh. 6 - Prob. 3APCh. 6 - Create a spreadsheet for computing, using Eq....Ch. 6 - Prob. 5APCh. 6 - Create a spreadsheet for computing the velocity of...
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- 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.arrow_forwardProblem 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_forward
- Problem 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_forwardI 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_forward
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