Fluid Mechanics: Fundamentals and Applications
4th Edition
ISBN: 9781259696534
Author: Yunus A. Cengel Dr., John M. Cimbala
Publisher: McGraw-Hill Education
expand_more
expand_more
format_list_bulleted
Question
Chapter 7, Problem 21P
To determine
The primary dimensions of each additive term in the given equation.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
SAE 30 oil at 20 °C flows at 1.8 ft3/s from a reservoir into a6-in-diameter pipe. Use flat-plate theory to estimate theposition x where the pipe wall boundary layers meet in thecenter. Compare with Eq.,
Le/d≈ 0.06 Red laminar
and give some explanationsfor the discrepancy.
We are given laboratory data, taken by Prof. Robert Kirchhoffand his students at the University of Massachusetts, for thespin rate of a 2-cup anemometer. The anemometer wasmade of ping-pong balls ( d = 1.5 in) split in half, facing inopposite directions, and glued to thin ( 1/4-in) rods pegged toa center axle. There were fourrods, of lengths l = 0.212, 0.322, 0.458, and 0.574 ft. Theexperimental data, for wind tunnel velocity U and rotationrate Ω , are as follows:
Assume that the angular velocity Ω of the device is afunction of wind speed U , air density ρ and viscosity μ , rodlength l , and cup diameter d . For all data, assume air is at1 atm and 20 ° C. Defi ne appropriate pi groups for thisthe problem, and plot the data in this dimensionless manner.Comment on the possible uncertainty of the results.As a design application, suppose we are to use thisanemometer geometry for a large-scale ( d = 30 cm) airportwind anemometer. If wind speeds vary up to 25 m/s and wedesire an average…
In deriving the vorticity equation, we have used the identity divergence x (divergence P) = 0
Show that this identity is valid for any scalar lamda by checking it in Cartesian and cylindrical coordinates.
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
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- Assume an inviscid, incompressible flow. Also, standard sea level density and pressure are 1.23 kg/m3 (0.002377 slug/ft3) and 1.01 × 105 N/m2 (2116 lb/ft2), respectively. Consider the nonlifting flow over a circular cylinder of a given radius,where V∞ = 20 ft/s. If V∞ is doubled, that is, V∞ = 40 ft/s, does theshape of the streamlines change? Explain.arrow_forwardA curved blood vessel has an internal diameter ? = 5 mm and a radius of curvature of ?? = 17 mm. Blood has a density of ρ = 1060 kg/m3 and a viscosity of 3.5 cP, and travels at an average velocity of ? = 1 m/s. a) Comment on the nature of the flow with reference to relevant non-dimensional groups. b) Can the flow be modelled using the Hagen-Poisseuile equation? If not, explain what specific assumptions are invalid. c) The viscosity of blood is measured and is shown in Figure Q2. Consider two long straight blood vessels with steady flow. The diameter of the first vessel is 5 mm and the average velocity is 6 cm/s. The internal diameter of the second vessel is 2.2 mm and the average velocity is 50 cm/s. Which vessel would you expect the Hagen-Poisseiulle equation to be more accurate in? Explain your answer (1-2 sentences).arrow_forwardWhen fluid in a long pipe starts up from rest at a uniformacceleration a , the initial flow is laminar. The flow undergoesa transition to turbulence at a time t * which depends, tofirst approximation, only upon a , ρ , and μ . Experiments by P. J. Lefebvre, on water at 20 8 C starting from rest with 1-gacceleration in a 3-cm-diameter pipe, showed transition att * = 1.02 s. Use this data to estimate ( a ) the transition timeand ( b ) the transition Reynolds number Re D for water flowaccelerating at 35 m/s 2 in a 5-cm-diameter pipe.arrow_forward
- 3.3 Starting with a small fluid element of volume dx dy dz, derive the continuity equation (Eq. 3.4) in rectangular cartesian coordinates.arrow_forwardthe 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_forwardDefine the following dimensionless group number in fluid mechanics, a)Interpretation of force ratio, and what types of application. b)Reynolds number (Re) c)Euler number (Eu) d) Mach number (Ma) e) Weber number (We)arrow_forward
- When a flow is considered incompressible what assumption is being made regarding fluid properties? The answer was: Density is assumed to remain constant I want to know why is this the answer?arrow_forwardWhat is the most general form of a purely radial polarcoordinate incompressible flow pattern, υ r = υ r ( r , θ , t ) andυ θ = 0, that satisfies continuity?arrow_forwardA smooth 12-cm-diameter sphere is immersed in a streamof 20°C water moving at 6 m/s. The appropriate Reynoldsnumber of this sphere is approximately(a) 2.3 E5, (b) 7.2 E5, (c) 2.3 E6, (d) 7.2 E6, (e) 7.2 E7arrow_forward
- Define variable flow? Also discuss the forces encoundered in fluid mechanics?arrow_forward3a) a) Explain and discuss, the concept of velocity boundarylayer and its importance in Fluid Mechanics.arrow_forwardVortices are usually shed from the rear of a cylinder, which are placed in a uniform flow at low speeds. The vortices alternatively leave the top and the bottom of the cylinder, as shown in figure, causing an alternating force normal because of generating a dimensionless relationship for Kármán vortex shedding frequency fk (1/s) as a function of free-stream speed V(m/s), fluid density r (kg/m3), fluid viscosity µ (kg/m.s), sound velocity c (m/s), surface roughness ɛ (m) and cylinder diameter D(m). Solve the problem by making the necessary assumptions and drawing the schematic figure. I-Determine the nondimensional p parameters using repeating variables, involving f, ɛ, c and µ as nonrepeating variables ii-the dynamics of Bhosphorus bridge is investigated in a wind tunnel for the vortex generation behind the wires. A 1/56,2 scaled down model of the hanging wires is used in the laboratory. If vortex shedding frequency of of Bhosphorus bridge 562 Hz is measured in the laboratory at…arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning
Principles of Heat Transfer (Activate Learning wi...
Mechanical Engineering
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Cengage Learning
Intro to Compressible Flows — Lesson 1; Author: Ansys Learning;https://www.youtube.com/watch?v=OgR6j8TzA5Y;License: Standard Youtube License