Fluid Mechanics: Fundamentals and Applications
4th Edition
ISBN: 9781259696534
Author: Yunus A. Cengel Dr., John M. Cimbala
Publisher: McGraw-Hill Education
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Chapter 7, Problem 124P
To determine
The primary dimensions of gas constant R over universal gas constant Ru.
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The primary dimensions of the universal gas constant Ru are (a) m·L/t2·T (b) m2·L/N (c) m·L2/t2·N·T (d ) L2/t2·T (e) N/m·t
Q3: Analyze the primary dimensions of the universal ideal gas constant Rµ using the ideal gas law, Pv = nR, T where P is pressure, v is volume, T is absolute temperature, and n is the number of moles of the gas.
Consider the following mass distribution, where x- and y- coordinates are given in meters: 5.0 kg at (0.0, 0.0) m, 5.0 kg at (0.0, 6.0) m, and 3.0 kg at (8.0, 0.0) m. Where should a fourth object of 5.0 kg be placed so that the center of gravity of the four- object arrangement will be at (0.0, 0.0) m? Enter the y-coordinate.
Chapter 7 Solutions
Fluid Mechanics: Fundamentals and Applications
Ch. 7 - What is the difference between a dimension and a...Ch. 7 - List the seven primary dimensions. What is...Ch. 7 - Write the primary dimensions of the universal...Ch. 7 - Write the primary dimensions of each of the...Ch. 7 - Prob. 5PCh. 7 - Prob. 6PCh. 7 - Prob. 7PCh. 7 - On a periodic chart of the elements, molar mass...Ch. 7 - Prob. 9PCh. 7 - The moment of force(M)is formed by the cross...
Ch. 7 - You are probably familiar with Ohm law for...Ch. 7 - Write the primary dimensions of each of the...Ch. 7 - Prob. 13PCh. 7 - Thermal conductivity k is a measure of the ability...Ch. 7 - Write the primary dimensions of each of the...Ch. 7 - Prob. 16PCh. 7 - Explain the law of dimensional homogeneity in...Ch. 7 - Prob. 18PCh. 7 - Prob. 19PCh. 7 - An important application of fluid mechanics is the...Ch. 7 - Prob. 21PCh. 7 - Prob. 22PCh. 7 - In Chap. 4, we defined the material acceleration,...Ch. 7 - Newton's second law is the foundation for the...Ch. 7 - What is the primary reason for nondimensionalizing...Ch. 7 - Prob. 26PCh. 7 - In Chap. 9, we define the stream function for...Ch. 7 - In an oscillating incompressible flow field the...Ch. 7 - Prob. 29PCh. 7 - Consider ventilation of a well-mixed room as in...Ch. 7 - In an oscillating compressible flow field the...Ch. 7 - List the three primary purposes of dimensional...Ch. 7 - List and describe the three necessary conditions...Ch. 7 - A student team is to design a human-powered...Ch. 7 - Repeat Prob. 7-34 with all the same conditions...Ch. 7 - This is a follow-tip to Prob. 7-34. The students...Ch. 7 - The aerodynamic drag of a new sports car is lo be...Ch. 7 - This is a follow-tip to Prob. 7-37E. The...Ch. 7 - Consider the common situation in which a...Ch. 7 - Prob. 40PCh. 7 - Some students want to visualize flow over a...Ch. 7 - A lightweight parachute is being designed for...Ch. 7 - Prob. 43PCh. 7 - Prob. 44PCh. 7 - Prob. 45PCh. 7 - The Richardson number is defined as Ri=L5gV2...Ch. 7 - Prob. 47PCh. 7 - Prob. 48PCh. 7 - A stirrer is used to mix chemicals in a large tank...Ch. 7 - Prob. 50PCh. 7 - Albert Einstein is pondering how to write his...Ch. 7 - Consider filly developed Couette flow-flow between...Ch. 7 - Consider developing Couette flow-the same flow as...Ch. 7 - The speed of sound c in an ideal gas is known to...Ch. 7 - Repeat Prob. 7-54, except let the speed of sound c...Ch. 7 - Repeat Prob. 7-54, except let the speed of sound c...Ch. 7 - Prob. 57PCh. 7 - When small aerosol particles or microorganisms...Ch. 7 - Prob. 59PCh. 7 - Prob. 60PCh. 7 - Prob. 61PCh. 7 - An incompressible fluid of density and viscosity ...Ch. 7 - Prob. 63PCh. 7 - In the study of turbulent flow, turbulent viscous...Ch. 7 - Bill is working on an electrical circuit problem....Ch. 7 - A boundary layer is a thin region (usually along a...Ch. 7 - A liquid of density and viscosity is pumped at...Ch. 7 - A propeller of diameter D rotates at angular...Ch. 7 - Repeat Prob. 7-68 for the case an which the...Ch. 7 - Prob. 70PCh. 7 - Prob. 71PCh. 7 - Consider a liquid in a cylindrical container in...Ch. 7 - Prob. 73PCh. 7 - One of the first things you learn in physics class...Ch. 7 - Prob. 75CPCh. 7 - Prob. 76CPCh. 7 - Define wind tunnel blockage. What is the rule of...Ch. 7 - Prob. 78CPCh. 7 - Prob. 79CPCh. 7 - In the model truck example discussed in Section...Ch. 7 - Prob. 83PCh. 7 - A small wind tunnel in a university's...Ch. 7 - There are many established nondimensional...Ch. 7 - Prob. 86CPCh. 7 - For each statement, choose whether the statement...Ch. 7 - Prob. 88PCh. 7 - Prob. 89PCh. 7 - Prob. 90PCh. 7 - Prob. 91PCh. 7 - From fundamental electronics, the current flowing...Ch. 7 - Prob. 93PCh. 7 - Prob. 94PCh. 7 - The Archimedes number listed in Table 7-5 is...Ch. 7 - Prob. 96PCh. 7 - Prob. 97PCh. 7 - Prob. 98PCh. 7 - Prob. 99PCh. 7 - Prob. 100PCh. 7 - Repeal Prob. 7-100 except for a different...Ch. 7 - A liquid delivery system is being designed such...Ch. 7 - Prob. 103PCh. 7 - Au aerosol particle of characteristic size DPmoves...Ch. 7 - Prob. 105PCh. 7 - Prob. 106PCh. 7 - Prob. 107PCh. 7 - Prob. 108PCh. 7 - Prob. 109PCh. 7 - Prob. 110PCh. 7 - Repeat pall (a) of Prob. 7-110, except instead of...Ch. 7 - Sound intensity I is defined as the acoustic power...Ch. 7 - Repeal Prob. 7-112, but with the distance r from...Ch. 7 - Engineers at MIT have developed a mechanical model...Ch. 7 - Prob. 116PCh. 7 - Prob. 117PCh. 7 - An electrostatic precipitator (ESP) is a device...Ch. 7 - Prob. 119PCh. 7 - Prob. 120PCh. 7 - Prob. 121PCh. 7 - Prob. 122PCh. 7 - Prob. 123PCh. 7 - Prob. 124PCh. 7 - The primary dimensions of kinematic viscosity are...Ch. 7 - There at four additive terms in an equation, and...Ch. 7 - Prob. 127PCh. 7 - Prob. 128PCh. 7 - Prob. 129PCh. 7 - A one-third scale model of a car is to be tested...Ch. 7 - Prob. 131PCh. 7 - A one-third scale model of an airplane is to be...Ch. 7 - Prob. 133PCh. 7 - Prob. 134PCh. 7 - Consider a boundary layer growing along a thin...Ch. 7 - Prob. 136P
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- Write the primary dimensions of the universal ideal gas constant Ru. (Hint: Use the ideal gas law, PV = nRuT where P is pressure, V is volume, T is absolute temperature, and n is the number of moles of the gas.)arrow_forwardWe define the specific ideal gas constant Rgas for a particular gas as the ratio of the universal gas constant and the molar mass (also called molecular weight) of the gas, Rgas = Ru/M. For a particular gas, then, the ideal gas law is written as follows: PV = mRgasT or P = ρRgasT where P is pressure, V is volume, m is mass, T is absolute temperature, and ? isthedensityoftheparticulargas.Whatare the primary dimensions of Rgas? For air, Rair = 287.0 J/kg·K in standard SI units. Verify that these units agree with your result.arrow_forwardWhich one is not a primary dimension? (a) Velocity (b) Time (c) Electric current (d ) Temperature (e) Massarrow_forward
- In the following section, at least 2 to up to 5 answers may be correct. 1) For a fluid, the assumption (simplifying notion) of incompressibility has important consequences: Pascal’s principle: a change of pressure in an enclosed fluid at rest is transmitted undiminished to all points in the fluid. pressure changes are transmitted immediately from one place to another. the speed of sound then is infinite (just within this approximation). pressure becomes unpredictable. none of the above. 2) Archimedes’ principle can be summarized as: an immersed object is buoyed up by a force equal to the weight of the fluid it displaces. a bathtub is fun, and may lead to important physical discoveries regarding the volume of an object and how much water it displaces, and the weight of that amount of water. boats swim because of the work done by sailors. submarines are always doomed. fish swim because they are less heavy than water 3) A…arrow_forwardDimensional Analysis and Hydraulic Similitude (fluid mechanics) 1. Water at 60F at 12 ft/s in a 6-in. pipe. (a) For dynamic similarity, determine the velocity of medium fuel oil at 90F flowing in a 12-in. pipe. (b) Determine the diameter of the pipe that should be used if a medium lubricating oil at 70oF if flowing at a velocity of 50 ft/s. find the: a. velocity : ____________________ fps b. diameter : ____________________ in.arrow_forwardWrite the primary dimensions of each of the following variables from the field of thermodynamics, showing all your work: (a) energy E; (b) specific energy e = E/m; (c) power W . .arrow_forward
- For most gases at standard or near standard conditions, the relationshipamong pressure, density, and temperature is given by the perfect gasequation of state: p = ρRT, where R is the specific gas constant. For airat near standard conditions, R = 287 J/(kg · K) in the International System of Units and R = 1716 ft · lb/(slug · ◦R) in the English Engineering System of Units. Using the above information, consider the following two cases: a. At a given point on the wing of a Boeing 727, the pressure andtemperature of the air are 1.9 × 104 N/m2 and 203 K, respectively.Calculate the density at this point.b. At a point in the test section of a supersonic wind tunnel, the pressureand density of the air are 1058 lb/ft2 and 1.23 × 10−3 slug/ft3,respectively. Calculate the temperature at this point.arrow_forwardThe Reynold's number of a sphere falling in air is 1E6. If the sphere's radius is 1ft, what is its velocity? Density of air is 0.00234 slug/ft³ and viscosity of air is 3.8E-7 lbf-sec/ft²A. 2.5 ft/sB. 5.1 ft/sC. 40.6 ft/sD. 81.2 ft/sarrow_forwardFluid mechanics, I need solutions in 15 minutes please. MCQ/Determine the horizontal and vertical components of the liquid pressure acting on the semicylindrical gate ABC, as shown in the figure. The width into the paper is 1 m. A-Fx = 257.430 kN and Fy = 59.801 kN B-Fx = 164.018 KN and Fy = 37.229 KN C-Fx = 269.894 kN and Fy = 65.526 KN D-Fx = 98.182 kN and Fy = 20.002 KN E-Fx = 234.789 kN and Fy = 52.418 kN F-Fx = 187.005 kN and Fy = 42.182 KN G-Fx = 119.956 kN and Fy = 25.550 KN H-Fx = 141.327 kN and Fy = 31.171 KN I-Fx = 288.147 kN and Fy = 69.098 KN J-Fx = 213.112 kN and Fy = 47.903 KNarrow_forward
- Here, a liquid's density is to be determined by a 1-cm diameter cylindrical hydrometer whose division marks are non visable. The hydrometer is first dropped in water, and the water level is marked. The hydrometer is then dropped into the 'liquid x', and it is observed that the mark for water has risen 0.85 cm above the liquid–air interface. In this case, the height of the originalwater mark is 12.7 cm. As such, how would I determine the density of the liquid?arrow_forwardThe Stokes-Oseen formula for drag force on a sphere at low speed is given asD = 3dV +916V 2d2, where D is drag, V is velocity, is density, d is the sphere diameter, and is the viscosity coe¢ cient.(a) Using the formula given, Önd the dimensions of the viscosity coe¢ cient. (Donít simply look upthe dimensions; use the formula to show them.) Be sure to show your work. Find the primaryunits of viscosity in SI and British units.(b) Verify that the Stokes-Oseen formula is dimensionally homogeneous.arrow_forwardFLUID MECHANICS : HYDROSTATICS Answer: 218kN, 180kN, 191kNarrow_forward
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