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 96P
To determine
The dimensional parameter generated by the given quantities.
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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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- Consider a three-dimensional, incompressible, irrotationalfl ow. Use the following two methods to prove that theviscous term in the Navier-Stokes equation is identicallyzero: (a) using vector notation; and (b) expanding out thescalar terms and substituting terms from the defi nition ofirrotationality.arrow_forwardHow does the Navier-Stokes equation encapsulate the complexities of fluid behavior, and what challenges arise when attempting to solve it in the context of mechanical engineering's fluid mechanicsarrow_forwardOil, of density ρ and viscosity μ , drains steadily down theside of a vertical plate, as in Fig. P4.80. After a developmentregion near the top of the plate, the oil fi lm willbecome independent of z and of constant thickness δ .Assume that w = w ( x ) only and that the atmosphere offersno shear resistance to the surface of the fi lm. ( a ) Solve theNavier-Stokes equation for w ( x ), and sketch its approximateshape. ( b ) Suppose that fi lm thickness δ and the slopeof the velocity profi le at the wall [ ∂ w /∂ x ] wall are measuredwith a laser-Doppler anemometer (Chap. 6). Find anexpression for oil viscosity μ as a function of ( ρ , δ , g ,[ ∂ w / ∂ x ] wall ).arrow_forward
- Fluid from a large reservoir at temperature T 0 fl ows into acircular pipe of radius R . The pipe walls are wound with anelectric resistance coil that delivers heat to the fl uid at a rateq w (energy per unit wall area). If we wish to analyze thisproblem by using the full continuity, Navier-Stokes, andenergy equations, what are the proper boundary conditionsfor the analysis?arrow_forwardA viscous liquid of constant ρ and μ falls due to gravitybetween two plates a distance 2 h apart, as in Fig. P4.37. Thefl ow is fully developed, with a single velocity component w = w ( x ). There are no applied pressure gradients, onlygravity. Solve the Navier-Stokes equation for the velocityprofi le between the plates.arrow_forwardA flow field is described in Cartesian coordinates by Is it incompressible?arrow_forward
- Is the Lagrangian method of fluid flow analysis more similar to study of a system or a control volume? Explain.arrow_forwardDefine vorticity in terms of the vector velocity field. How is the “rotation” of a fluid particle related to its vorticity? In Cartesian coordinates, write down the general form of the z-component of vorticity. What is the condition on the vector velocity field such that a flow is irrotational?arrow_forwardIn this chapter, we make a statement that the boundary layer approximation “bridges the gap” between the Euler equation and the Navier–Stokes equation. Explainarrow_forward
- the differential equation for conservation of mass, the continuity equation. In cylindrical coordinates, and for steady flow, 1/ r ∂(rur) /∂r + 1/ r ∂u? /∂? + ∂uz /∂z = 0 Write the primary dimensions of each additive term in the equation, and verify that the equation is dimensionally homogeneous. Show all your work.arrow_forwardFor Couette fl ow between a moving and a fi xed plate,Fig. 4.12 a , solve continuity and Navier-Stokes to fi nd thevelocity distribution when there is slip at both walls.arrow_forwardWhat is the main difference between the steady, incompressible Bernoulli equation for irrotational regions of flow, and the steady incompressible Bernoulli equation for rotational but inviscid regions of flow?arrow_forward
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