Explanation Write the group of physical variables. Write the unknown function. f ( p , m , p 0 , r , ρ , E V ) = 0 Here, Pressure is p , mass is m , initial pressure is p 0 , spherical radius is r , density is ρ , and bulk modulus of the water is E V . The total number of variables ( n ) is 6. The number of base dimensions ( m ) is 3 . The q -variables (single variable) is p , ρ and E V . Refer Table 8-1 , write the F - L - T (force-length-time) dimensions for the variables as in Table (1). Quantity Symbol M - L - T Pressure p M L − 1 T − 2 mass m M Initial pressure p 0 M L − 1 T − 2 radius r L Density ρ M L − 3 bulk modulus E V M L − 1 T − 2 Calculate the number of II terms. n − m = 6 − 3 = 3 Thus, there are 3 II terms. Select V , A , and ρ as repeating variables ( m = 3 ) because it contains all three primary dimensions ( M - L - T ) . Perform the dimensional analysis. Write the first II ( II 1 ) term. II 1 = p 0 a m b r c p (I) Here, constants are a , b , and c respectively. Substitute p 0 = M L − 1 T − 2 , m = M , r = L , and p = M L − 1 T − 2 in Equation (I). II 1 = ( M L − 1 T − 2 ) a ( M ) b ( L ) c ( M L − 1 T − 2 ) = ( M a + b + 1 ) ( L − a + c − 1 ) ( T − 2 a − 2 ) (II) Solve Equation (II) to get the value of M , L and T . a + b + 1 = 0 − a + c − 1 = 0 − 2 a − 2 = 0 } (III) Balance the equation (III) to get the following relation between the constant. a = − 1 b = 0 c = 0 Substitute a = − 1 , b = 0 , and c = 0 in Equation (I). II 1 = p 0 − 1 m 0 r 0 p = p p 0 Write the second II ( II 2 ) term. II 2 = p 0 d m e r f ρ (IV) Here, constants are d , e , and f respectively. Substitute p 0 = M L − 1 T − 2 , m= M , r = L , and ρ = M L − 3 in Equation (IV). II 2 = ( M L − 1 T − 2 ) d ( M ) e ( L ) f ( M L − 3 ) = ( M d + e + 1 ) ( L − d + f − 3 ) ( T − 2 d ) (V) Here, the II terms are dimensionless

2nd Edition

ISBN: 9780134649290

Author: Russell C. Hibbeler

Publisher: PEARSON

See similar textbooks

Concept explainers

Properties of Fluids

The term fluid represents a type of substance that can easily change its shape under any external pressure/force and can flow. Fluids can acquire any shape in which it is stored and can resist normal stresses but cannot resist shear stress in rest condit…

Videos

Question

Chapter 8, Problem 36P

To determine

The relation between p and these parameters m,p0,r,ρ, and EV.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8, Problem 35P

Chapter 8, Problem 37P

Students have asked these similar questions

1- A manufacturing company is optimizing the cooling time of a newly developed plastic molding process. The goal is to minimize the total production cost, which depends on the cooling time (t) in minutes. The production cost (C, in dollars) is given by: C=50+10(t)-0.5(t)^2 where: 5 st≤ 20 (cooling time in minutes) Using the Two-Experiments Sequential Method (up to five cycles) find the optimal cooling time (t) that minimizes the production cost. 3:29 م

2- Find the optimum minimum point of y = x²-6x + 2 in the interval 0 ≤ x ≤ 10 using sequential search method with three experiments. the accuracy a = 0.06. 3- Find the optimum of y = 9x -0.1 x² in the interval 0 ≤ x ≤ 100, and α = 0.05 Use two and three experiments sequential search methods?

hand-written solutions only please

Chapter 8 Solutions

Fluid Mechanics (2nd Edition)

Ch. 8 - Prob. 1P Ch. 8 - Prob. 2P Ch. 8 - Prob. 3P Ch. 8 - Prob. 4P Ch. 8 - Prob. 5P Ch. 8 - Prob. 6P Ch. 8 - The pressure change that occurs in the aortic...Ch. 8 - Express the group of variables L, μ, ρ, V as a...Ch. 8 - Prob. 9P Ch. 8 - Prob. 10P

Ch. 8 - Prob. 11P Ch. 8 - Prob. 12P Ch. 8 - Prob. 13P Ch. 8 - The speed of sound V in air is thought to depend...Ch. 8 - Prob. 15P Ch. 8 - Prob. 16P Ch. 8 - Prob. 17P Ch. 8 - Prob. 18P Ch. 8 - The discharge Q over the weir A depends upon the...Ch. 8 - Prob. 20P Ch. 8 - Prob. 21P Ch. 8 - Prob. 22P Ch. 8 - Prob. 23P Ch. 8 - Prob. 24P Ch. 8 - As the liquid drains from the pipette, the exit...Ch. 8 - The discharge Q from a turbine is a function of...Ch. 8 - The flow of air Q through the fan is a function of...Ch. 8 - The drag FD on the square plate held normal to the...Ch. 8 - Prob. 29P Ch. 8 - Prob. 30P Ch. 8 - Prob. 31P Ch. 8 - The head loss hL in a pipe depends upon its...Ch. 8 - Prob. 33P Ch. 8 - The change in pressure Δp in the pipe is a...Ch. 8 - The drag FD on the automobile is a function of its...Ch. 8 - Prob. 36P Ch. 8 - Prob. 37P Ch. 8 - The diameter D of oil spots made on a sheet of...Ch. 8 - Prob. 39P Ch. 8 - The height H of water as it passes over a small...Ch. 8 - Water and crude oil flow through the pipes with a...Ch. 8 - Prob. 42P Ch. 8 - If the water in a river is flowing at 16 ft/s, and...Ch. 8 - Prob. 44P Ch. 8 - Prob. 45P Ch. 8 - Prob. 46P Ch. 8 - Prob. 47P Ch. 8 - Prob. 48P Ch. 8 - The flow of water around the structural support is...Ch. 8 - If the drag on a 15-m-long airplane is to be...Ch. 8 - Prob. 51P Ch. 8 - A 15-ft-long submarine is intended to travel at 15...Ch. 8 - The flow of water around the bridge pier is to be...Ch. 8 - Prob. 54P Ch. 8 - Prob. 55P Ch. 8 - Prob. 56P Ch. 8 - Prob. 57P Ch. 8 - Prob. 58P Ch. 8 - The jet plane can fly at Mach 2 in 40°F air. What...Ch. 8 - Prob. 60P Ch. 8 - The drag coefficient on an airplane is defined by...Ch. 8 - Prob. 62P Ch. 8 - Prob. 63P Ch. 8 - Prob. 64P Ch. 8 - A ship has a length of 180 m and travels in the...

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

SEE MORE QUESTIONS

Recommended textbooks for you

Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY

Elements Of Electromagnetics

Mechanical Engineering

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Oxford University Press

Mechanics of Materials (10th Edition)

Mechanical Engineering

ISBN:9780134319650

Author:Russell C. Hibbeler

Publisher:PEARSON

Thermodynamics: An Engineering Approach

Mechanical Engineering

ISBN:9781259822674

Author:Yunus A. Cengel Dr., Michael A. Boles

Publisher:McGraw-Hill Education

Control Systems Engineering

Mechanical Engineering

ISBN:9781118170519

Author:Norman S. Nise

Publisher:WILEY

Mechanics of Materials (MindTap Course List)

Mechanical Engineering

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Cengage Learning

Engineering Mechanics: Statics

Mechanical Engineering

ISBN:9781118807330

Author:James L. Meriam, L. G. Kraige, J. N. Bolton

Publisher:WILEY

SEE MORE TEXTBOOKS

Properties of Fluids: The Basics; Author: Swanson Flo;https://www.youtube.com/watch?v=TgD3nEO1iCA;License: Standard YouTube License, CC-BY

Fluid Mechanics-Lecture-1_Introduction & Basic Concepts; Author: OOkul - UPSC & SSC Exams;https://www.youtube.com/watch?v=6bZodDnmE0o;License: Standard Youtube License

The relation between p and these parameters m , p 0 , r , ρ , and E V .

Concept explainers

Videos

The relation between p and these parameters m,p0,r,ρ, and EV.

Want to see the full answer?

Chapter 8 Solutions