Fluid Mechanics (2nd Edition)
2nd Edition
ISBN: 9780134649290
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 4, Problem 64P
To determine
The rate at which the level of gasoline is rising in the tank.
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(a) Find a second-order homogeneous linear ODE for which the given functions are
solutions. (b) Show linear independence by the Wronskian. (c) Solve the initial value
problem.
a. cos(5x), sin(5x), y(0) = 3, y'(0) = −5
b. e-2.5x cos(0.3x), e-2.5x sin(0.3x), y(0) = 3, y'(0) = -7.5
Solve the IVP.
a. y" 16y 17e* ;
=
y(0) = 6,
y'(0) = -2
b. (D² + 41)y = sin(t) + ½ sin(3t) + sin(t) ; y(0) = 0, y'(0) :
=
35
31
Find the general solution.
a. y' 5y = 3ex - 2x + 1
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b. y" +4y' + 4y = e¯*cos(x)
c. (D² + I)y = cos(wt), w² # 1
Chapter 4 Solutions
Fluid Mechanics (2nd Edition)
Ch. 4 - Prob. 1FPCh. 4 - Air flows through the triangular duct at 0.7 kg/s...Ch. 4 - Water has an average velocity of 8 m/s through the...Ch. 4 - Crude oil flows through the pipe at 0.02 m3/s. If...Ch. 4 - Determine the mass flow of air having a...Ch. 4 - Prob. 6FPCh. 4 - The velocity of the steady flow at A and B is...Ch. 4 - Prob. 8FPCh. 4 - As air exits the tank at 0.05 kg/s, it is mixed...Ch. 4 - Water flows along the triangular channel having...
Ch. 4 - Determine the mass flow of nitrogen in an...Ch. 4 - Nitrogen gas flows through the 8-in.-diameter...Ch. 4 - Air enters the turbine of a jet engine at a rate...Ch. 4 - Determine the mass flow of air in the duct if it...Ch. 4 - Prob. 6PCh. 4 - Prob. 7PCh. 4 - Prob. 8PCh. 4 - The velocity profile of a liquid flowing through...Ch. 4 - Prob. 10PCh. 4 - Prob. 11PCh. 4 - Determine the mass flow of the fluid if it has the...Ch. 4 - The liquid in the rectangular channel has a...Ch. 4 - The liquid in the rectangular channel has a...Ch. 4 - Water flows along the semicircular trough with an...Ch. 4 - The 30-mm-diameter nozzle ejects water such that...Ch. 4 - Determine the volumetric flow through the...Ch. 4 - Determine the volumetric flow through the...Ch. 4 - The human heart has an average discharge of...Ch. 4 - Prob. 20PCh. 4 - Prob. 21PCh. 4 - Kerosene flows through the nozzle at 0.25 m3/s....Ch. 4 -
Kerosene flows through the nozzle at 0.25 m3/s....Ch. 4 - At two specific instants during a heartbeat, the...Ch. 4 - Prob. 25PCh. 4 - The radius of the circular duct varies as m,...Ch. 4 - Prob. 27PCh. 4 - Prob. 28PCh. 4 - The average velocities of water flowing steadily...Ch. 4 - Air flows through the tapered duct, and during...Ch. 4 - Prob. 31PCh. 4 - Air is pumped into the tank, and at the instant...Ch. 4 - Prob. 33PCh. 4 - Prob. 34PCh. 4 - Compressed air is being released from the tank,...Ch. 4 - Prob. 36PCh. 4 - Prob. 38PCh. 4 - Water flows through the pipe at A at 60 kg/s, and...Ch. 4 - Prob. 40PCh. 4 - Prob. 41PCh. 4 - Nitrogen flows into the tank at A at VA = 3 m/s,...Ch. 4 - Nitrogen flows into the tank at A at VA = 3 m/s,...Ch. 4 - The flat strip is sprayed with paint using the six...Ch. 4 - Prob. 45PCh. 4 - Prob. 46PCh. 4 - Drilling fluid is pumped down through the center...Ch. 4 - Drilling fluid is pumped down through the center...Ch. 4 - Oil flows into the pipe at A with an average...Ch. 4 - The unsteady flow of glycerin is such that at A it...Ch. 4 - The unsteady flow of glycerin is such that at A it...Ch. 4 - Prob. 52PCh. 4 - Prob. 53PCh. 4 - The cylindrical plunger traveling at Vp =...Ch. 4 - The cylindrical plunger traveling at Vp =...Ch. 4 - Prob. 56PCh. 4 - The pressure vessel of a nuclear reactor is filled...Ch. 4 - With every breath, air enters the trachea, its...Ch. 4 - A liquid flows through the drainpipe such that it...Ch. 4 - Oil flows into a mixing tank through pipe A with...Ch. 4 - Oil flows into the mixing tank through pipe A at...Ch. 4 - Water flows into the tank through two pipes. At A...Ch. 4 - Gasoline flows into the tank through two pipes. At...Ch. 4 - Prob. 64PCh. 4 - The cylindrical syringe is actuated by applying a...Ch. 4 - Prob. 66PCh. 4 - The tank contains air at a temperature of 20°C and...Ch. 4 - The natural gas (methane) and crude oil mixture...Ch. 4 - Prob. 69PCh. 4 - Prob. 70PCh. 4 - Prob. 71PCh. 4 - Prob. 72PCh. 4 - Prob. 73PCh. 4 - Prob. 74PCh. 4 - Kerosene flows into the 4-ft-diameter cylindrical...Ch. 4 - Prob. 76PCh. 4 - Water flows into the cylindrical tank through...Ch. 4 - Water flows into the cylindrical tank through...Ch. 4 - The cylinder is pushed down into the tube at a...Ch. 4 - Prob. 80PCh. 4 - Prob. 81PCh. 4 - Prob. 82PCh. 4 - Prob. 83PCh. 4 - Prob. 84PCh. 4 - Oil flows into the trapezoidal container at a...Ch. 4 - Oil flows into the conical frustum at a constant...Ch. 4 - Water in the triangular trough is at a depth of y...Ch. 4 - Prob. 88PCh. 4 - Prob. 89PCh. 4 - Prob. 90PCh. 4 - Prob. 91PCh. 4 - Hydrogen is pumped into the closed cylindrical...Ch. 4 - Hydrogen is pumped into the closed cylindrical...Ch. 4 - Prob. 94PCh. 4 - A part is manufactured by placing molten plastic...
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