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 23P
Derive an expression for the drag force on a smooth object moving through compressible fluid if this force depends only on speed and size of object, and viscosity, density, and modulus of elasticity 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…
A 1:20 scaled-down model of a hydrofoil is tested in a water channel, at a velocity of 0.179 m/s. At this velocity, a drag force of 2.2 N is measured. Determine the drag force of the original hydrofoil, at a velocity of 0.8 m/s.
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).
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 1:20 scale down model of a hydrofoil is tested in a water channel, at velocity of 0.179 m/s. At this velocity, a drag force of 2.2 N is measured. Determine the drag force of the original hydrofoil, at velocity of 0.8 m/s.arrow_forwardAn automobile has a characteristic length and area of 8 ft and 60 ft2, respectively. When tested in sea-level standard air, it has measured velocities of 20, 40, and 60 mi/h and drag forces of 31, 115, and 249 lbf, respectively. The same car travels in Colorado at 115 mi/h at an altitude of 3500 m. Using dimensional analysis, estimate its drag force (in lbf). Using dimensional analysis, estimate the horsepower required to overcome air drag (in hp)arrow_forward(c) In a wind tunnel experiment, a drag force on 1:8 scale model billboard is 1 kN. The air in the wind tunnel is 20 degree Celsius. During a storm, the wind speed can reach 20 km/hr with air temperature of 10 degree Celsius. Determine the drag force experience by the billboard during storm. Refer Appendix B.arrow_forward
- A 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_forwardQ 3. A submarine of length 160 m, average diameter of 15 m moves through seawater with kinematic viscosity 1.5x10-6 m²/s and density 1025 kg/m3 at 9.5 m/s. Estimate the power needed to overcome the drag force. Consider the submarine as a fat plate that has the same surface area as the submarine.arrow_forwardA fighter aircraft is to operate at 200 m/s in air at standard conditions ( = 1.2 kg/m3). Amodel is constructed to 1/20 scale (length ratio) and tested in a wind tunnel at the sameair temperature (same air viscosity) to determine the drag force. The drag force FD is afunction of the air density and viscosity , the velocity V and the cross section length ofthe airplane D.arrow_forward
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