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
Videos
Question
Chapter 7, Problem 78CP
To determine
Whether the data given data is sufficient for researchersto reach the Reynolds's number.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
An underwater device which is 2m long is to be moved at 4 m/sec. If a geometrically
similar model 40 cm long is tested in a variable pressure wind tunnel at a speed of 60
m/sec with the following information,
Poir at Standard atmospheric pressure = 1.18kg/m³
Pwater = 998kg/m3
Hair = 1.80 x 10-5 Pa-s at local atmospheric pressure and
Hwater = 1 × 10-3 Pa-s then the pressure of the air in the model used
times local atmospheric pressure
is
An engineer is to design a human powered submarine for a design competition. The overall length of the prototype submarine is 2.24 m and its engineer designers hope that it can travel fully submerged through water at 0.560 m/s. The water is freshwater (a lake) at 7-15°C (p=999.1 kg/m3 and u= 1.138 ×103 kg/m-st. The design team builds a one-eighth scale model to test in their university's wind tunnel. The air in the wind tunnel is at 25°C (p= 1.180 kg/m3 and u = 1.849 ×10-5 kg/m-s) and at one standard atmosphere pressure. At what air speed do they need to run the wind tunnel in order to achieve similarity?
A- Womersley number (a) of a human aorta is 20 and for the rabbit aorta is 17, the blood density is approximately the same across the species. The values of viscosity were 0.0035 Ns/m² for the human and 0.0040 Ns/m² for the rabbit. The diameter of the aorta is 2.0 cm for the man, and 0.7 cm for the rabbit, estimate the heart rate beats per minute (bpm) for both species
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
- The drag force on a submarine, which is moving on the surface, is to be determined by a test on a model which is scaled down to one-twentieth of the prototype. The test is to be carried in a towing tank, where the model submarine is moved along a channel of liquid. The density and the kinematic viscosity of the seawater are 1010 kg/m³ and 1.3x10-6 m 2/s, respectively. The speed of the prototype is 2.6 m/s. Assume that F = f(V, L. g. p.), using pi-theorem and similarity principle to: a) Determine the speed at which the model should be moved in the towing tank. b) Determine the kinematic viscosity of the liquid that should be used in the towing tank.arrow_forwardWe want to predict the drag force on a remote-control airplane as it flies through air having a density of 1.21 kg/m³ and a viscosity of 1.76x10- Pa-s. The airplane's fuselage has a diameter of 200 mm and the airplane will fly through air at a speed of 32 m/s. A model of the airplane's fuselage will be tested in a pressurized wind tunnel. The diameter of the model is 75 mm and the density and viscosity of the air in the wind tunnel are 3.00 kg/m³ and 1.82× 10-5 Pa-s, respectively. a) The diameter of the airplane's fuselage will be used to define the Reynolds number Re, for the flow around the fuselage. Compute the Reynolds number for the flow around the airplane's fuselage (answer: Re, = 4.40x 10'). b) Find the speed of the air that should be used to test a model of the fuselage in the wind tunnel to correctly model dynamic conditions (answer: 35.6 m/s). c) The model is tested in the wind tunnel at four speeds that bracket the speed computed above. The measured drag forces on the…arrow_forwardHere, a 1:10 scale prototype of a propeller on a ship is to be tested in a water channel. What would the rotating speed of the model be if the rotational speed of the p propeller is 2000 rpm, and if: (a) the Froude number governs the model-prototype similarity(b) Reynolds number governs the similarityarrow_forward
- Ship whose full length is 100 m is to travel at 10 m/sec. For dynamical similarity, with what velocity should a 1:25 model of the ship be towed?arrow_forwardWrite the primary dimensions of each of the following variables from the field of solid mechanics, showing all your work: (a) moment of inertia I; (b) modulus of elasticity E, also called Young’s modulus; (c) strain ? ; (d) stress ?. (e) Finally, show that the relationship between stress and strain (Hooke’s law) is a dimensionally homogeneous equation.arrow_forwardAir at 20 °C forms a boundary layer near a solid wall, in which the velocity profile is sinusoidal (see Fig. 1-14). The boundary-layer thickness is 7 mm and the peak velocity is 9 m/s. Compute the shear stress in the boundary layer at y equal to (a) 0, (b) 3.5 mm, and (c) 7 mm. 7 mm Vmax = 9 m/s Peak Sine wave Fig. 1-14arrow_forward
- (b) A Formula 1 team tests their car in a wind tunnel at a scale of 50%, at a speed of Vwinarunnet = 50 m/s. The measured downforce at this speed is Foownforce.WT = 3000 N and the model reference area is Aref wT = 0.5 m?. 1. Find the downforce magnitude on the full-scale race car at the same Reynolds number. Assume constant air density p = 1.2 kg/m. II. It is said that F1 cars could travel upside down, as shown below. At what speed should the full-scale car travel to achieve this, if its mass is m = 740 kg? The acceleration of gravity is g = 9.81 m/s?. Downforce Weightarrow_forward7-67 A liquid of density p and viscosity u is pumped at volume flow rate b through a pump of diameter D. The blades of the pump rotate at angular velocity w. The pump supplies a pressure rise AP to the liquid. Using dimensional analysis, generate a dimensionless relationship for AP as a function of the other parameters in the problem. Identify any established nondimensional parameters that appear in your result. Hint: For consistency (and whenever possible), it is wise to choose a length, a density, and a velocity (or angular velocity) as repeating variables.arrow_forwardMott ." cometer, which we can analyze later in Chap. 7. A small ball of diameter D and density p, falls through a tube of test liquid (p. µ). The fall velocity V is calculated by the time to fall a measured distance. The formula for calculating the viscosity of the fluid is discusses a simple falling-ball vis- (Po – p)gD² 18 V This result is limited by the requirement that the Reynolds number (pVD/u) be less than 1.0. Suppose a steel ball (SG = 7.87) of diameter 2.2 mm falls in SAE 25W oil (SG = 0.88) at 20°C. The measured fall velocity is 8.4 cm/s. (a) What is the viscosity of the oil, in kg/m-s? (b) Is the Reynolds num- ber small enough for a valid estimate?arrow_forward
- A tanker 300 m long is to be tested by a 1: 50 scale model. If the ship is to travel at 46 km/h, at what speed must the model be towed to obtain dynamic similarity (neglecting friction) with its prototype?arrow_forwardThe drag of a sonar transducer is to be predicted, based on wind (Air) tunnel test data. The prototype is 1.5 m diameter sphere, is to be towed at 4.3 m/s in seawater. The model is 0.2 m diameter. Take: Air density = 1.2 kg/m, Air dynamic viscosity = 1.81 x 10$ Pa. s, seawater density = 1000 kg/m, seawater dynamic viscosity 1.813x 10 Pa s, If the drag of the model at these test conditions is 9.5 N, estimate the drag of the prototype in (N).arrow_forwardA student team is to design a human-powered submarine for a design competition. The overall length of the prototype submarine is 95 (m), and its student designers hope that it can travel fully submerged through water at 0.440 m/s. The water is freshwater (a lake) at T = 15°C. The design team builds a one-fifth scale model to test in their university’s wind tunnel. A shield surrounds the drag balance strut so that the aerodynamic drag of the strut itself does not influence the measured drag. The air in the wind tunnel is at 25°C and at one standard atmosphere pressure. At what air speed do they need to run the wind tunnel in order to achievesimilarity?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