04: Use dimensional analysis to show that in a problem involving shallow water waves (Figure 1), both the Froude number (Fr Ta) and the Reynolds number Vgh pch, are relevant dimensionless parameters Fr = f (Re). The wave speed c of (Re = waves on the surface of a liquid is a function of depth h, gravitational acceleration g, fluid density p, and fluid viscosity µ.

04: Use dimensional analysis to show that in a problem involving shallow water waves (Figure 1), both the Froude number (Fr Ta) and the Reynolds number Vgh pch, are relevant dimensionless parameters Fr = f (Re). The wave speed c of (Re = waves on the surface of a liquid is a function of depth h, gravitational acceleration g, fluid density p, and fluid viscosity µ.

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.

Chapter5: Analysis Of Convection Heat Transfer

Section: Chapter Questions

Problem 5.13P: 5.13 The torque due to the frictional resistance of the oil film between a rotating shaft and its...

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5.13 The torque due to the frictional resistance of the oil film between a rotating shaft and its bearing is found to be dependent on the force F normal to the shaft, the speed of rotation N of the shaft, the dynamic viscosity of the oil, and the shaft diameter D. Establish a correlation among these variables by using dimensional analysis.
Q4: Use dimensional analysis to show that in a problem involving shallow water waves (Figure 1), both the Froude number (Fr = and the Reynolds number (Re pch. are relevant dimensionless parameters Fr = f (Re). The wave speed c of %3D waves on the surface of a liquid is a function of depth h, gravitational acceleration g, fluid density p, and fluid viscosity u. P. u Figure 1
Q4: Use dimensional analysis to show that in a problem involving shallow water waves (Figure 1), both the Froude number (Fr T) and the Reynolds number %3| Vgh (Re = pch are relevant dimensionless parameters Fr = f (Re). The wave speed c of waves on the surface of a liquid is a function of depth h, gravitational acceleration g, fluid density p, and fluid viscosity u. P.u Figure 1
3- Use dimensional analysis to show that in a problem involving shallow water waves, both the Froude number and the Reynolds number are relevant dimensionless parameters. The wave speed c of waves on the surface of a liquid is a function of depth h, gravitational acceleration g. fluid density p, and fluid viscosity μ. Manipulate your's to get the parameters into the following form: Fr= √=f(Re) where Re=pch μ h Too 8 P₂ μ
A2) In order to solve the dimensional analysis problem involving shallow water waves as in Figure 2, Buckingham Pi Theorem has been used. h Figure 2 Through the observation that has been done, the wave speed © of waves on the surface of a liquid is a function of the depth (h), gravitational acceleration (g), fluid density (p), and fluid viscosity (µ). By using this Buckingham Pi Theorem: a) Analyze the above problem and show that the Froude Number (Fr) and Reynolds Number (Re) are the relevant dimensionless parameters involve in this problem. b) Manipulate your Pi (1) products to get the parameter into the following form: pch := f(Re) where Re = Fr = c) If one additional primary variable parameter involve in this proolem such as, temperature (T). Discuss on the Pi (m) products that can be produce and explain why this dimensional analysis is very important in the experimental work.
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Dimensional analysis: O Is very helpful in determining speeds for dynamic similarity in model testing O Is an efficient way of storing and retrieving experimental data All responses are correct Helps in planning experiments Can be used to derive equations and non-dimensional numbers