Concept explainers
Heat flux The heat flow
61.
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- Find the constant of proportionality. z is directly proportional to the sum of x and y. If x=2 and y=5, then z=28.arrow_forwardTsunami 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?arrow_forwardFourier'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 fluxarrow_forwardFourier'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 net outward heat flux SSF•nds= - kff triple 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.) G S VT.n dS across the boundary S of D. It may be easier to use the Divergence Theorem and evaluate aarrow_forwardEXERCISE 2.2 An automobile follows a circular road whose radius is 50 m. Let x and y respectively denote the eastern and northern directions, with origin at the center of the circle. Suppose the vehicle starts from rest at x = 50 m heading north, and its speed depends on the distance s it travels according to v=0.5s-0.0025s², where s is measured in meters and v is in meters per second. It is known that the tires will begin to skid when the total acceleration of the vehicle is 0.6g. Where will the automobile be and how fast will it be going when it begins to skid? Describe the position in terms of the angle of the radial line relative to the x axis.arrow_forwardbo Find (xT x)" xT y where, b2 40 57 112 45 54 118 50 54 128 55 60 121 60 66 126 65 59 136 70 61 144 75 58 142 80 59 149 85 56 165 S SINARLINEarrow_forwardarrow_back_iosarrow_forward_ios
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