Fox and McDonald's Introduction to Fluid Mechanics
9th Edition
ISBN: 9781118912652
Author: Philip J. Pritchard, John W. Mitchell
Publisher: WILEY
expand_more
expand_more
format_list_bulleted
Textbook Question
Chapter 7, Problem 35P
A large tank of liquid under pressure is drained through a smoothly contoured nozzle of area A. The mass flow rate is thought to depend on nozzle area, A, liquid density, ρ, difference in height between the liquid surface and nozzle, h, tank gage pressure, Δp, and gravitational acceleration, g. Determine how many independent Π parameters can be formed for this problem. Find the dimensionless parameters. State the functional relationship for the mass flow rate in terms of the dimensionless parameters.
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 E is subjected to a fluid crossflow of velocity V, density p, and viscosity u. Its center deflection & is assumed to be a function of all these variables. Part A-Rewrite this proposed function 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
help
Chapter 7 Solutions
Fox and McDonald's Introduction to Fluid Mechanics
Ch. 7 - The slope of the free surface of a steady wave in...Ch. 7 - One-dimensional unsteady flow in a thin liquid...Ch. 7 - In atmospheric studies the motion of the earths...Ch. 7 - Fluid fills the space between two parallel plates....Ch. 7 - By using order of magnitude analysis, the...Ch. 7 - Consider a disk of radius R rotating in an...Ch. 7 - An unsteady, two-dimensional, compressible,...Ch. 7 - Experiments show that the pressure drop for flow...Ch. 7 - At very low speeds, the drag on an object is...Ch. 7 - We saw in Chapter 3 that the buoyant force, FB, on...
Ch. 7 - Assume that the velocity acquired by a body...Ch. 7 - Derive by dimensional analysis an expression for...Ch. 7 - The speed of shallow water waves in the ocean...Ch. 7 - The speed, V, of a free-surface wave in shallow...Ch. 7 - The boundary-layer thickness, , on a smooth flat...Ch. 7 - The speed, V, of a free-surface gravity wave in...Ch. 7 - Derive an expression for the velocity of very...Ch. 7 - Derive an expression for the axial thrust exerted...Ch. 7 - Derive an expression for drag force on a smooth...Ch. 7 - The energy released during an explosion, E, is a...Ch. 7 - Measurements of the liquid height upstream from an...Ch. 7 - The load-carrying capacity, W, of a journal...Ch. 7 - Derive an expression for the drag force on a...Ch. 7 - A circular disk of diameter d and of negligible...Ch. 7 - Two cylinders are concentric, the outer one fixed...Ch. 7 - The time, t, for oil to drain out of a viscosity...Ch. 7 - You are asked to find a set of dimensionless...Ch. 7 - A continuous belt moving vertically through a bath...Ch. 7 - Derive an expression for the frictional torque...Ch. 7 - Tests on the established flow of six different...Ch. 7 - The power, P, required to drive a fan is believed...Ch. 7 - The sketch shows an air jet discharging...Ch. 7 - The diameter, d, of bubbles produced by a...Ch. 7 - Choked-flow nozzles are often used to meter the...Ch. 7 - A large tank of liquid under pressure is drained...Ch. 7 - Spin plays an important role in the flight...Ch. 7 - The power loss, P, in a journal bearing depends on...Ch. 7 - The thrust of a marine propeller is to be measured...Ch. 7 - The rate dT/dt at which the temperature T at the...Ch. 7 - When a valve is closed suddenly in a pipe with...Ch. 7 - An airship is to operate at 20 m/s in air at...Ch. 7 - An airplane wing of 3 m chord length moves through...Ch. 7 - A flat plate 1.5 m long and 0.3 m wide is towed at...Ch. 7 - This 1:12 pump model using water at 15C simulates...Ch. 7 - An ocean-going vessel is to be powered by a...Ch. 7 - On a cruise ship, passengers complain about the...Ch. 7 - A 1:3 scale model of a torpedo is tested in a wind...Ch. 7 - A flow rate of 0:18 m3/s of water at 20C...Ch. 7 - A force of 9 N is required to tow a 1:50 ship...Ch. 7 - An airplane wing, with chord length of 1.5 m and...Ch. 7 - A water pump with impeller diameter of 24 in. is...Ch. 7 - A model hydrofoil is to be tested at 1:20 scale....Ch. 7 - A ship 120 m long moves through freshwater at 15C...Ch. 7 - A 1:30 scale model of a cavitating overflow...Ch. 7 - In some speed ranges, vortices are shed from the...Ch. 7 - A 1:8 scale model of a tractor-trailer rig is...Ch. 7 - On a cruise ship, passengers complain about the...Ch. 7 - When a sphere of 0.25 mm diameter and specific...Ch. 7 - The flow about a 150 mm artillery projectile which...Ch. 7 - Your favorite professor likes mountain climbing,...Ch. 7 - A 1:50-scale model of a submarine is to be tested...Ch. 7 - Consider water flow around a circular cylinder, of...Ch. 7 - A 1:10 scale model of a tractor-trailer rig is...Ch. 7 - The power, P, required to drive a fan is assumed...Ch. 7 - Over a certain range of air speeds, V, the lift,...Ch. 7 - The pressure rise, p, of a liquid flowing steadily...Ch. 7 - An axial-flow pump is required to deliver 0.75...Ch. 7 - A model propeller 1 m in diameter is tested in a...Ch. 7 - Consider Problem 7.38. Experience shows that for...Ch. 7 - Closed-circuit wind tunnels can produce higher...Ch. 7 - A 1:16 model of a bus is tested in a wind tunnel...Ch. 7 - The propagation speed of small-amplitude surface...
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
- Problem 5 s): The discharge pressure (P) of a screw pump (Fig. 5) is a function of flow rate (Q), screw diameter (D), fluid viscosity (u) and screw angular speed (w). P = f (Q, D, μ, w). Use the pi theorem to rewrite this function in terms of dimensionless parameters, ₁ g (T₂). Choose Q, D, and u as repeating variables. Screw Fig. 5: Screw pumparrow_forward1. The thrust of a marine propeller Fr depends on water density p, propeller diameter D, speed of advance through the water V, acceleration due to gravity g, the angular speed of the propeller w, the water pressure p, and the water viscosity μ. You want to find a set of dimensionless variables on which the thrust coefficient depends. In other words CT = FT · = ƒen(#1, #2, ...) pV2D2 (a) What is k? Explain. (b) Find the 's on the right-hand-side of equation 1 if one of them HAS to be a Froude number gD/V², (1)arrow_forwardUse image below Solve carefully QUESTION DOWN BELOWarrow_forward
- The differential equation for small-amplitude vibrations y(r, f) of a simple beam is given by a*y + E = 0 ax pA where p = beam material density A = cross-sectional area I= area moment of inertia E = Young's modulus Use only the quantities p, E, and A to nondimensionalize y, x, and t, and rewrite the differential equation in dimensionless form. Do any parameters remain? Could they be removed by further manipulation of the variables?arrow_forwardc) The drag force Fp on a cylinder of diameter d and length / is to be studied. What functional form relates the dimensionless variables if a fluid with velocity V flows normal to the cylinder?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 true optionarrow_forward4 Discharge, Q through a venturimeter depends on the following variable Inlet pipe diameter - D Throat diameter - d Pressure drop across the venturimeter - Ap Fluid density - P Dynamic viscosity - µ Using MLT set of dimensions evaluate the dimensionless parameters correlating this phenomenon 5 The droplet size, D produced by a liquid spray nozzle depends on the following variable Nozzle diameter - d Jet velocity - U Fluid density - p Dynamic viscosity – u Surface tension - o Using MLT set of dimensions evaluate the dimensionless parameters correlating this phenomenonarrow_forwardThis pleasearrow_forward
- Task 1 (d) The force, F, of a turbine generator is a function of density p, area A and velocity v. By assuming F = apª A® vc and dimensional homogeneity, find a, b and c and express F in terms of p, A and v. (a, a, b and c are real numbers). Make the following assumptions to determine the dimensionless parameter: F = 1k N if the scalar values of pAv= 1milli. (e) The dynamic coefficient of viscosity µ (viscosity of a fluid) is found from the formula: µAv F = Fis the force exerted on the liquid, A is the cross sectional area of the path, v is the fluid velocity and l is the distance travelled by the fluid. Using dimensional analysis techniques, determine the equation that governs µ and its dimensions using the results of (b) and the equation in c, clearly showing all steps in the dimensional analysis.arrow_forwardFluid Mechanics Problem: Assume all fluids are 20oC.arrow_forwardAt low velocities (laminar flow), the volume flow Q through a small-bore tube is a function only of the tube radius R, the fluid viscosity u, and the pressure drop per unit tube length dp/dx. Using the pi theorem, find an appropriate dimensionless relationship.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
Unit Conversion the Easy Way (Dimensional Analysis); Author: ketzbook;https://www.youtube.com/watch?v=HRe1mire4Gc;License: Standard YouTube License, CC-BY