Heat transfer Fourier’s Law of heat transfer (or heat conduction) states that the heat flow
42. T(x, y, z) = 100 + x2 + y2 + z2;
D = {(x, y, z): 0 ≤ x ≤ 1, 0 ≤ 1, 0 ≤ z ≤ 1}
Want to see the full answer?
Check out a sample textbook solutionChapter 17 Solutions
EP CALCULUS:EARLY TRANS.-MYLABMATH 18 W
Additional Math Textbook Solutions
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Calculus and Its Applications (11th Edition)
Calculus & Its Applications (14th Edition)
Precalculus Enhanced with Graphing Utilities (7th Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
- 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?arrow_forwardFind 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_forwardFind the constant of proportionality. y is directly proportional to x. If x=30, then y=15.arrow_forward
- 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?arrow_forwardDefine Newton’s Law of Cooling. Then name at least three real-world situations where Newton’s Law of Cooling would be applied.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 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 thearrow_forward
- Ab. 56 Advanced matharrow_forwardOhm's law states that the voltage drop Vacross an ideal resistor is linearly proportional to the current i flowing through the resistor as V= iR. Where R is the resistance. However, real resistors may not always obey Ohm's law. Suppose that you perform some very precise experiments to measure the voltage drop and the corresponding current for a resistor. The following results suggest a curvilinear relationship rather than the straight line represented by Ohm's law. i -1 - 0.5 - 0.25 0.25 0.5 1 V -637 -96.5 -20.25 20.5 96.5 637 Instead of the typical linear regression method for analyzing such experimental data, fit a curve to the data to quantify the relationship. Compute V for i = 0.1 using Polynomial Interpolation.arrow_forwardOhm's law states that the voltage drop Vacross an ideal resistor is linearly proportional to the current i flowing through the resistor as V= iR. Where R is the resistance. However, real resistors may not always obey Ohm's law. Suppose that you perform some very precise experiments to measure the voltage drop and the corresponding current for a resistor. The following results suggest a curvilinear relationship rather than the straight line represented by Ohm's law. i -1 - 0.5 - 0.25 0.25 0.5 1 V -637 -96.5 -20.25 20.5 96.5 637 Instead of the typical linear regression method for analyzing such experimental data, fit a curve to the data to quantify the relationship. Compute V for i = 0.1 using Newton's Divided Difference Method.arrow_forward
- The drag force, Fp, acting on an immersed body by a moving fluid can be calculated as PU? 2 where C, is the drag coefficient, A is the projected area of the body on a plane normal to the Fp = CpA flow, p is the mass density of the fluid, and U is the undisturbed velocity of the fluid. Suppose Cp, A, and p are known constants of values 0.6, 10 ft2, and 1.94 slug/ft, respec- tively. U is a lognormal random variable with parameters hy and Sy. Determine the distribution of Fp-arrow_forwardTransient Orifice Flow: Water is discharged from a reservoir through a long pipe as shown. By neglecting the change in the level of the reservoir, the transient velocity of the water flowing from the pipe, vt), can be expressed as: - Reservoir v(t) V2gh = tanh V2gh) Pipe Where h is the height of the fluid in the 7- reservoir, L is the length of the pipe, g is the acceleration due to gravity, and t is the time elapsed from the beginning of the flow Transient Orifice Flow: Determine the helght of the fluid in the reservoir at time, t= 2.5 seconds, given that the velocity at the outfall, vt) = 3 m/s, the acceleration due to gravity, g = 9.81 m/s? and the length of the pipe to outfall, L= 1.5 meters. Reservoir v(t) V2gh = tanh 2L 2gh water Pipe Hint: Transform the equation to a function of form: fih) = 0 Solve MANUALLY using BISECTION AND REGULA-FALSI METHODS, starting at xn = 0.1, Kg =1, E = 0.001 and If(*new)l < Earrow_forwardNeed asap pls. Thanks.arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning