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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Chapter 7, Problem 11P
Assume that the velocity acquired by a body falling from rest (without resistance) depends on weight of body, acceleration due to gravity, and distance of fall. Prove by dimensional analysis that
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A block and sphere are connected by a cord that passes over a pulley as shown. Neglect friction and assume the cord is massless.
Take m₁
= 2.00 kg, m₂ = 5.45 kg, and 8 = 48.5⁰.
m₂
m₂
(a) What are the magnitude of acceleration (in m/s2) of the block and sphere?
m/s²
(b) What is the tension (in N) in the cord? (Enter the magnitude.)
N
(c) What is the speed (in m/s) of each object 2.50 s after being released from rest?
m/s
(d) What If? If the incline under m₂ is rough, what is the minimum value of the coefficient of static friction for which the
system will not move?
Ms=
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1,V
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The direction of friction force
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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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- Blocks m1 = 4.0 kg and m2 = 1.0 kg are connected by a thin, light cord which is draped over a light pulley so that mass u= 0 m¡ is hanging over the edge of the pulley as shown. The surface between m2 and the table is essentially frictionless. What is the acceleration (in m/s²) of the blocks? (Take g=10 m/s²) m2 mi 4 2 10 6. 8 O Oarrow_forwardA block of mass m slides along a horizontal surface lubricated with a thick oil which providesa drag force proportional to the square root of velocity.F_d=-bv^1/2If v = v0 at t = 0, determine v as a function of timearrow_forwardYou are called as an expert witness in a trial for a traffic violation. The facts are these: A driver slammed on his brakes and came to a stop with constant acceleration. Measurements of his tires and the skid marks on the pavement indicate that he locked his car’s wheels, the car traveled 192 ft before stopping, and the coefficient of kinetic friction between the road and his tires was 0.750. He was charged with speeding in a 45 mi>h zone but pleads innocent. What is your conclusion: guilty or innocent? How fast was he going when he hit his brakes?arrow_forward
- A cord passing over a pulley connects two masses, as shown, where m1 = 3.80 kg and m2 = 7.20 kg. The system accelerates with a magnitude of 0.94 m/s2. The coefficient of kinetic friction between the masses and the incline is the same for both masses. Assume the pulley is frictionless, and the cord is massless. (Due to the nature of this problem, do not use rounded intermediate values in your calculations—including answers submitted in WebAssign.) What is the tension (in N) in the cord?arrow_forwardThe 3,000lb race car is up and running again and slides into a wall at 150mph. What is the kinetic energy of the vehicle at impact? Why is the coefficient of fiction not required?arrow_forwardMost of you have seen car advertisements where the car manufacturerbrags about how fast one of its cars can go from 0 to 100 km/h. Accordingto the manufacturer, the BMW 750iL model can go from 0 to 100 km/h in6.7 seconds. This performance is usually measured on a test track. The engine in the car is rated at 243 kW at 5000 rpm. The car has a reported weight of 23 kN . Is the claim by the manufacturer justifiable? Well, to answer this question you may agree it would be more fun to drive toa BMW dealership and take the car for a test run on a racing track. But let us answer this question with the knowledge you have gained so far in this course. We need to make some assumptions first; we can assume that the driver weighs 900 N and the reported weight of the car includes enough gasoline for this test. Next, we convert the speed and the mass values into appropriate units.arrow_forward
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