Shallow-water velocity equationa. Confirm that the linear approximation to f(x) = tanh x ata = 0 is L(x) = x.b. Recall that the velocity of a surface wave on the ocean2ndtanh -In fluid dynamics, shallowis v =water refers to water where the depth-to-wavelength ratiod/A < 0.05. Use your answer to part (a) to explain why theshallow water velocity equation is v = Vgd.c. Use the shallow-water velocity equation to explain whywaves tend to slow down as they approach the shore.

a. Suppose that is 'f' differentiable on an interval l containing the point α. The linear…

Answered: Shallow-water velocity equation a.…

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter7: Forced Convection Inside Tubes And Ducts

Section: Chapter Questions

Problem 7.35P

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Under laminar conditions, the volume flow Q through asmall triangular-section pore of side length b and length Lis a function of viscosity μ , pressure drop per unit length∆p / L , and b . Using the pi theorem, rewrite this relation indimensionless form. How does the volume flow change ifthe pore size b is doubled?
What is the definition of a timeline? How can timelines be produced in a water channel? Name an application where timelines are more useful than streaklines.
The flow rate of water in a garden hose is measured using the bucket-andstopwatch method. Filling a 5-L bucket takes 75 seconds. If the inner diameter of the hose is 10 mm and the density and viscosity of water are approximately 998 kg m-3 and 0.9 cP, respectively, (a) is the flow inside the hose laminar or turbulent? (b) If the flow rate is adjusted such that the flow is with Re = 2100, how long would it take to fill the same bucket?
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This problem is useful for the preliminary design of a hydroturbine. From the material learned in this chapter, it is fairly simple to estimate how much power a hydroturbine can generate, given only the flow rate of water and the elevation difference upstream and downstream of the dam. A dam has a gross head of 15.5 m and a flow rate of 0.22 m3 /s. Approximating the overall efficiency of the turbine/generator to be 75%, estimate the electrical power (in kW) that couldbe produced.
Develop an equation for the transmitted wave height behind a vertical wall extending a depth d into the water of depth h, based on the concept that the wall allows the wave power below depth d to propagate past. Qualitatively, do you believe that your equation for the transmitted wave height will under- or overestimate the actual wave height ? Discuss your results.
A curved blood vessel has an internal diameter ? = 5 mm and a radius of curvature of ?? = 17 mm. Blood has a density of ρ = 1060 kg/m3 and a viscosity of 3.5 cP, and travels at an average velocity of ? = 1 m/s. a) Comment on the nature of the flow with reference to relevant non-dimensional groups. b) Can the flow be modelled using the Hagen-Poisseuile equation? If not, explain what specific assumptions are invalid. c) The viscosity of blood is measured and is shown in Figure Q2. Consider two long straight blood vessels with steady flow. The diameter of the first vessel is 5 mm and the average velocity is 6 cm/s. The internal diameter of the second vessel is 2.2 mm and the average velocity is 50 cm/s. Which vessel would you expect the Hagen-Poisseiulle equation to be more accurate in? Explain your answer (1-2 sentences).
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Q. What is meant by the term “velocity of circulation” and explain its relevance in the quantity equation.
Apply the necessary conversion factors to prove the relationship between dimensionless turbine specific speed and customary U.S. turbine specific speed, NSt = 43.46NSt, US. Note that we assume water as the fluid and standard earth gravity.

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