Fox and McDonald's Introduction to Fluid Mechanics
9th Edition
ISBN: 9781118912652
Author: Philip J. Pritchard, John W. Mitchell
Publisher: WILEY
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Textbook Question
Chapter 7, Problem 19P
Derive an expression for drag force on a smooth submerged object moving through incompressible fluid if this force depends only on speed and size of object and viscosity and density of the fluid.
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We 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…
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.
Consider a Falling Sphere Viscometer, which is used to measure the viscosity
μ of a fluid by observing the terminal velocity of a heavy sphere (density Ps
and diameter D) falling under gravity in a column of the fluid (density pf).
(a) Use Dimensional Analysis to derive a formula for the drag force
exerted on the sphere by the viscous fluid when it is moving at speed v
through the fluid.
(b) How is the terminal velocity of the sphere related to the fluid viscosity?
(c) If the sphere starts from rest, use Dimensional Analysis to predict the
timescale over which the sphere will reach its terminal velocity.
Please use dimensiona analysis to solve the problem
Answr for part a= Fd=KmuVD
answer for part b=V=Fd/kmuD
Please solve only for part C (part a and b no need to solve)and expalin in detail
Thanks
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...
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- A student needs to measure the drag on a prototype of characteristic length d, moving at velocity U, in air at sea-level conditions. She constructs a model of characteristic length dm such that the ratio d,/dm drag under dynamically similar conditions in sea-level air. The student claims that the drag force on the prototype will be = a factor f. She then measures the model identical to that of the model. Is her claim correct? Explain, showing your work (no credit for just guessing).arrow_forwardGlobal warming will produce rising sea levels partly due to melting ice caps and partly due to the expansion of water as average ocean temperatures rise. To get some idea of the size of this effect, calculate the change in length, Ah (in mm), of a column of water 1.5 km high for a temperature increase of 1.2 °C.Assume the column is not free to expand sideways. As a model of the ocean, that is a reasonable approximation, as only parts of the ocean very close to the surface can expand sideways onto land, and only to a limited degree. As another approximation, neglect the fact that ocean warming is not uniform with depth. Properties of water: 3 = 210 x 10 /C. c= 4186 J/kg - °C, L; = 334 kJ/kg, Le = 2256 kJ/kg Enter you answer below (to the nearest mm): Ah (in mm) = Type your answer.arrow_forwardA seA A, soA A solid cylinder of diameter d, length and density p, falls due to gravity inside a pipe of diameter D. The clearance between the solid cylinder and the pipe is filled with a Newtonian fluid of density p and u. For this clearance fluid, the terminal velocity of the cylinder is determined to be V, assuming a linear velocity profile. However, if the clearance fluid was changed to a Newtonian fluid of density 2p and viscosity 2u, then for an assumed linear velocity profile, the terminal velocity of the cylinder was determined to be V,. From the results of these experiments, one may write that (A) V = V (C) 2 V= V (B) V=2 V, (D) V= 4 Varrow_forward
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