Fluid Mechanics
8th Edition
ISBN: 9780073398273
Author: Frank M. White
Publisher: McGraw-Hill Education
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 5, Problem 5.14P
Flow in a pipe is often measured with an orifice plate, as in Fig. P5.14. The volume flow Q is a function of the pressure drop across the plate, the fluid density , the pipe diameter D, and the orifice diameter d. Rewrite this functional relationship in dimensionless form.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
A simply supported beam of diameter D, length L, and
modulus of elasticity Eis subjected to a fluid crossflow of
velocity V, density p, and viscosity u. Its center deflection
6 is assumed to be a function of all these variables. (a)
Rewrite this proposed function in dimensionless form, (b)
Suppose it is known that 6 is independent of u, inversely
proportional to E, and dependent only on pV2, not p and V
separately. Simplify the dimensionless function
accordingly. Hint: Take L, p, and Vas repeating variables,
P5.37
The volume flow Q through an orifice plate is a function of pipe diameter D, pressure
drop Ap across the orifice, fluid density p and viscosity u, and orifice diameter d. Using D, p,
and Ap as repeating variables, express this relationship in dimensionless form.
: The discharge pressure (P) of a gear pump (Fig. 3) is a function of flow rate (Q), gear diameter (D), fluid
viscosity (µ) and gear angular speed (w). P = f (Q, D, H, 0). Use the pi theorem to rewrite this function in terms of dimensionless
parameters.
Suction
Discharge
Fig. 3: Gear pump
P, Q
Chapter 5 Solutions
Fluid Mechanics
Ch. 5 - Prob. 5.1PCh. 5 - A prototype automobile is designed for cold...Ch. 5 - P5.3 The transfer of energy by viscous dissipation...Ch. 5 - When tested in water at 20°C flowing at 2 m/s, an...Ch. 5 - P5.5 An automobile has a characteristic length and...Ch. 5 - P5.6 The disk-gap-band parachute in the...Ch. 5 - Prob. 5.7PCh. 5 - Prob. 5.8PCh. 5 - The Richardson number, Ri, which correlates the...Ch. 5 - Prob. 5.10P
Ch. 5 - Prob. 5.11PCh. 5 - The Stokes number, St, used in particle dynamics...Ch. 5 - Prob. 5.13PCh. 5 - Flow in a pipe is often measured with an orifice...Ch. 5 - The wall shear stress T in a boundary layer is...Ch. 5 - P5.16 Convection heat transfer data are often...Ch. 5 - If you disturb a tank of length L and water depth...Ch. 5 - Prob. 5.18PCh. 5 - Prob. 5.19PCh. 5 - Prob. 5.20PCh. 5 - Prob. 5.21PCh. 5 - As will be discussed in Chap. 11, the power P...Ch. 5 - The period T of vibration of a beam is a function...Ch. 5 - Prob. 5.24PCh. 5 - The thrust F of a propeller is generally thought...Ch. 5 - A pendulum has an oscillation period T which is...Ch. 5 - Prob. 5.27PCh. 5 - Prob. 5.28PCh. 5 - P5.29 When fluid in a pipe is accelerated linearly...Ch. 5 - Prob. 5.30PCh. 5 - P5.31 The pressure drop per unit length in...Ch. 5 - A weir is an obstruction in a channel flow that...Ch. 5 - Prob. 5.33PCh. 5 - Prob. 5.34PCh. 5 - Prob. 5.35PCh. 5 - Prob. 5.36PCh. 5 - Prob. 5.37PCh. 5 - Prob. 5.38PCh. 5 - Prob. 5.39PCh. 5 - Prob. 5.40PCh. 5 - A certain axial flow turbine has an output torque...Ch. 5 - When disturbed, a floating buoy will bob up and...Ch. 5 - Prob. 5.43PCh. 5 - Prob. 5.44PCh. 5 - P5.45 A model differential equation, for chemical...Ch. 5 - P5.46 If a vertical wall at temperature Tw is...Ch. 5 - The differential equation for small-amplitude...Ch. 5 - Prob. 5.48PCh. 5 - P5.48 A smooth steel (SG = 7.86) sphere is...Ch. 5 - Prob. 5.50PCh. 5 - Prob. 5.51PCh. 5 - Prob. 5.52PCh. 5 - Prob. 5.53PCh. 5 - Prob. 5.54PCh. 5 - Prob. 5.55PCh. 5 - P5.56 Flow past a long cylinder of square...Ch. 5 - Prob. 5.57PCh. 5 - Prob. 5.58PCh. 5 - Prob. 5.59PCh. 5 - Prob. 5.60PCh. 5 - Prob. 5.61PCh. 5 - Prob. 5.62PCh. 5 - The Keystone Pipeline in the Chapter 6 opener...Ch. 5 - Prob. 5.64PCh. 5 - Prob. 5.65PCh. 5 - Prob. 5.66PCh. 5 - Prob. 5.67PCh. 5 - For the rotating-cylinder function of Prob. P5.20,...Ch. 5 - Prob. 5.69PCh. 5 - Prob. 5.70PCh. 5 - The pressure drop in a venturi meter (Fig. P3.128)...Ch. 5 - Prob. 5.72PCh. 5 - Prob. 5.73PCh. 5 - Prob. 5.74PCh. 5 - Prob. 5.75PCh. 5 - Prob. 5.76PCh. 5 - Prob. 5.77PCh. 5 - Prob. 5.78PCh. 5 - Prob. 5.79PCh. 5 - Prob. 5.80PCh. 5 - Prob. 5.81PCh. 5 - A one-fiftieth-scale model of a military airplane...Ch. 5 - Prob. 5.83PCh. 5 - Prob. 5.84PCh. 5 - *P5.85 As shown in Example 5.3, pump performance...Ch. 5 - Prob. 5.86PCh. 5 - Prob. 5.87PCh. 5 - Prob. 5.88PCh. 5 - P5.89 Wall friction Tw, for turbulent flow at...Ch. 5 - Prob. 5.90PCh. 5 - Prob. 5.91PCh. 5 - Prob. 5.1WPCh. 5 - Prob. 5.2WPCh. 5 - Prob. 5.3WPCh. 5 - Prob. 5.4WPCh. 5 - Prob. 5.5WPCh. 5 - Prob. 5.6WPCh. 5 - Prob. 5.7WPCh. 5 - Prob. 5.8WPCh. 5 - Prob. 5.9WPCh. 5 - Prob. 5.10WPCh. 5 - Given the parameters U,L,g,, that affect a certain...Ch. 5 - Prob. 5.2FEEPCh. 5 - Prob. 5.3FEEPCh. 5 - Prob. 5.4FEEPCh. 5 - Prob. 5.5FEEPCh. 5 - Prob. 5.6FEEPCh. 5 - Prob. 5.7FEEPCh. 5 - Prob. 5.8FEEPCh. 5 - In supersonic wind tunnel testing, if different...Ch. 5 - Prob. 5.10FEEPCh. 5 - Prob. 5.11FEEPCh. 5 - Prob. 5.12FEEPCh. 5 - Prob. 5.1CPCh. 5 - Prob. 5.2CPCh. 5 - Prob. 5.3CPCh. 5 - Prob. 5.4CPCh. 5 - Does an automobile radio antenna vibrate in...Ch. 5 - Prob. 5.1DPCh. 5 - Prob. 5.2DP
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
- 5.28 A simply supported beam of diameter D, length L, and modulus of elasticity E is subjected to a fluid crossflow of velocity V, density e, and viscosity u. Its center deflection d is assumed to be a function of all these variables. (a) Rewrite this proposed function in dimensionless form. (b) Suppose it is known that ô is independent of u, inversely proportional to E, and dependent only upon pl, notp and V separately. Simplify the dimensionless function accordingly.arrow_forwardQ1) Under laminar conditions, the volume flow rate Q through a small triangular-section pore of side length (b) and length (L) is a function of viscosity (u), pressure drop per unit length (AP/L), and (b). Using dimensional analysis to rewrite this relation. How does the volume flow changes if the pore size (b) is doubled?arrow_forwardP1.20 A baseball, with m = 145 g, is thrown directly upward from the initial position z = 0 and Vo = 45 m/s. The air drag on the ball is CV², as in Prob. 1.19, where C~ 0.0013 N: s*/m". Set up a differential equation for the ball motion, and solve for the instantaneous velocity V(t) and position z(1). Find the maximum height zmax reached by the ball, and compare your results with the classical case of zero air drag.arrow_forward
- 5.5 An automobile has a characteristic length and area of 8 ft and 60 ft, respectively. When tested in sea-level standard air, it has the following measured drag force versus speed: V, mi/h: 20 40 60 Drag, Ibf. 31 115 249 The same car travels in Colorado at 65 mi/h at an altitude of 3500 m. Using dimensional analysis, estimate (a) its drag force and (b) the horsepower required to overcome air drag.arrow_forwardYou are designing a spherical tank (Fig. P6.19) to hold water for a small village in a developing country. The volume of liquid it can hold can be computed as [3R – h] V = Th 3 where V = volume (m3), h = depth of water in tank (m), and R = the tank radius (m). If R = 3 m, what depth must the tank be filled to so that it holds 30 m3? Use three iterations of the Newton- Raphson method to determine your answer. Determine the approximate relative error after each iteration. Note that an initial guess of R will always converge. %3D FIGURE P6.19 Rarrow_forwardThe volume flow Q through an orifice plate is a function ofpipe diameter D , pressure drop D p across the orifice, fluiddensity ρ and viscosity μ , and orifice diameter d . Using D ,ρ , and ∆ p as r e peating variables, express this relationshipin dimensionless form.arrow_forward
- Buckingham Pi. A mechanical stirrer is used to mix chemicals in a large tank. The required shaft power P is a function of liquid density p, viscosity μ, stirrer blade diameter D, and angular speed w of the spinning blades. (a) use repeating variables p, D, u to find a relation between dimensionless power (1) and w (m2); (b,c) a small 1/3 scale model is used in water to predict the actual required power in a viscous liquid with SG =2 and μ = 12μwater. Find (b) the ratio of speeds, wwater/ wactual, necessary for dynamic similarity and then (c) the predicted ratio of powers Pwater/ Pactual. expecting unit : (a) π1 ~ D ; π^2 ~ D^2; (b) wwater/ wactual: 10^0; (c) Pwater/ Pactual 10^-3 SI constant Patm = 10^5 Pa; pwater - 1000 kg/m^3; pair ~ 1.2kg/m^3; µwater ~ 10^-3 N•s/m^2; pair - 2 x 10^-5 N•s/m^2 ; g = 9.8 m/s^2 =arrow_forwardThe drag force FD acting on a ship depends on the forward speed V , the fluid density ρ and viscosity µ, gravity, its length L and width B and the average roughness height k. (a) Use dimensional analysis to express this information in terms of a functional dependence on nondimensional groups. (b) If the ship moved from fresh water to salt water, where the density and viscosity are both increased by 10%, how would its drag force change at fixed speed?arrow_forwardThe power P generated by a certain windmill design depends upon its diameter D, the air density p, the wind velocity V, the rotation rate 0, and the number of blades n. (a) Write this relationship in dimensionless form. A model windmill, of diameter 50 cm, develops 2.7 kW at sea level when V= 40 m/s and when rotating at 4800 r/min. (b) What power will be developed by a geometrically and dynamically similar prototype, of diameter 5 m, in winds of 12 m/s at 2000 m standard altitude? (c) What is the appropriate rotation rate of the prototype?arrow_forward
- The wall shear stress Twin a boundary layer is assumed to be a function of stream velocity U, boundary layer thickness , local turbulence velocity u', density p, and local pressure gradient dp/dx. Using (p, U, and ) as repeating variables, rewrite this relationship as a dimensionless function.arrow_forwardQ.7. In an Aeroplan model of size 1/10 of its prototype the pressure drop is 7.5 kN/m². The model is tested in water. Find the corresponding pressure drop in the prototype. Take Density of air = 1.24 kg/m³. Density of water = 1000 kg/m³.Viscosity of air = 0.00018 poise Viscosity of water = 0.01 poisearrow_forwardThe thrust F of a Free propeller, either aircraft of marine, depends upon density ρ, the rotation rate n in r/s, the diameter D, and the forward velocity V. Viscous effects are slight and neglected here. Tests of a 25-cm-diameter model aircraft propeller, in a sea-level wind tunnel, yield the following thrust data at a velocity of 20 m/s : Rotation Rate, r/min____4800____6000____8000 Measured thrust, N____6.1____19____47 Use the dimensionless data to predict the thrust, in Newtons, of a similar 1.6-m-diameter prototype propeller when rotating at 3800 r/min and flying at 225 mi/h at 4000-m standard altitude.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher: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
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