Fourier's Law of heat transfer (or heat conduction) states that the heat flow vector F at a point is proportional to the negative gradient of the temperature: that is, F= -kVT, which means that heat energy flows from hot regions to cold regions. The constant k is calledthe conductivity, which has metric units of J/m-s-K or W/m-K. A temperature function T for a region D is given below. Find the net outward heat fluxSSF•nds= - kfftriple integral. Assume that k = 1.T(x,y,z)=110e-x²-y²-2².D is the sphere of radius a centered at the origin.The net outward heat flux across the boundary is.(Type an exact answer, using as needed.)GSVT.n dS across the boundary S of D. It may be easier to use the Divergence Theorem and evaluate a

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Answered: Fourier's Law of heat transfer (or heat…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 74E

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The kinetic energy E of an object varies jointly with the object’s mass m and the square of the object’s velocity v . An object with a mass of 50 kilograms traveling at 16 meters per second has a kinetic energy of 6400 joules. What is the kinetic energy of an object with a mass of 70 kilograms traveling at 20 meters per second?
Tsunami Waves and BreakwatersThis is a continuation of Exercise 16. Breakwaters affect wave height by reducing energy. See Figure 5.30. If a tsunami wave of height H in a channel of width W encounters a breakwater that narrows the channel to a width w, then the height h of the wave beyond the breakwater is given by h=HR0.5, where R is the width ratio R=w/W. a. Suppose a wave of height 8 feet in a channel of width 5000feet encounters a breakwater that narrows the channel to 3000feet. What is the height of the wave beyond the breakwater? b. If a channel width is cut in half by a breakwater, what is the effect on wave height? 16. Height of Tsunami WavesWhen waves generated by tsunamis approach shore, the height of the waves generally increases. Understanding the factors that contribute to this increase can aid in controlling potential damage to areas at risk. Greens law tells how water depth affects the height of a tsunami wave. If a tsunami wave has height H at an ocean depth D, and the wave travels to a location with water depth d, then the new height h of the wave is given by h=HR0.25, where R is the water depth ratio given by R=D/d. a. Calculate the height of a tsunami wave in water 25feet deep if its height is 3feet at its point of origin in water 15,000feet deep. b. If water depth decreases by half, the depth ratio R is doubled. How is the height of the tsunami wave affected?
Find the constant of proportionality. y is directly proportional to x. If x=30, then y=15.
Fourier's Law of heat transfer (or heat conduction) states that the heat flow vector F at a point is proportional to the negative gradient of the temperature: that is, F = − kVT, which means that heat energy flows from hot regions to cold regions. The constant k is called the conductivity, which has metric units of J/m-s-K or W/m-K. A temperature function T for a region D is given below. Find the SSF FondSk -KSS VT n dS across the boundary S of D. It may be easier to use the Divergence Theorem and evaluate a triple integral. Assume that k = 1. S S T(x,y,z) = 65e¯x² - y² − z²; net outward heat flux D is the sphere of radius a centered at the origin.
Fourier's Law of heat transfer (or heat conduction) states that the heat flow vector F at a point is proportional to the negative gradient of the temperature; that is, F = -KVT, which means that heat energy flows from hot regions to cold regions. The constant k is called the conductivity, which has metric units SS S of J/m-s-K or W/m-K. A temperature function T for a region D is given below. Find the net outward heat flux boundary S of D. It may be easier to use the Divergence Theorem and evaluate a triple integral. Assume that k = 1. T(x,y,z) = 100 - 5x+ 5y +z; D = {(x,y,z): 0≤x≤5, 0≤y≤4, 0≤z≤ 1} The net outward heat flux across the boundary is (Type an exact answer, using as needed.) -KSS S F.ndS = -k VT n dS across the
Fourier's Law of heat transfer (or heat conduction) states that the heat flow vector F at a point is proportional to the negative gradient of the temperature: that is, F = -kVT, which means that heat energy flows from hot regions to cold regions. The constant k is called FondSk the conductivity, which has metric units of J/m-s-K or W/m-K. A temperature function T for a region D is given below. Find the net outward heat flux
Ab. 56 Advanced math
Fluid runs through a drainage pipe with a 10-cm radius and a length of 10 m (1000 cm). The velocity of the fluid gradually decreases from the center of the pipe toward the edges as a result of friction with the walls of the pipe. For the data shown, v (x) is the velocity of the fluid (in cm/sec) and X represents the distance (in cm) from the center of the pipe toward the edge. 1 5 8 9 2 3 4 6 7 v (x) 195.9 195.2 194.2 192.7 190.8 188.4 185.6 182.3 178.6 174.5 Part: 0/ 4 Part 1 of 4 (a) The pipe is 10 m long (1000 cm). Determine how long it will take fluid to run the length of the pipe through the center of the pipe. Round to 1 decimal place. It will take fluid approximately 5.104 sec to run the length of the pipe through the center of the pipe. Part: 1/4 Part 2 of 4 (b) Determine how long it will take fluid at a point 9 cm from the center of the pipe to run the length of the pipe. Round to 1 decimal place. It will take fluid approximately sec to run the length of the pipe at a point 9…

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