04: Use dimensional analysis to show that in a problem involving shallow water waves (Figure 1), both the Froude number (Fr and the Reynolds number gh (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. C h P. u Figure 1

04: Use dimensional analysis to show that in a problem involving shallow water waves (Figure 1), both the Froude number (Fr and the Reynolds number gh (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. C h P. u Figure 1

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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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
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.
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
The velocity V of propagation of ripples on the surface of a shallow liquid depends on the gravitational acceleration g and the liquid depth h. If Buckingham's Theorem is used to identify the salient dimensionless group(s), how many dimensionless group(s) will be obtained? Number of dimensionless group(s) = 1. {1} (Enter your answer as a number.)
Pide Use Buckingham's PI Theorem to determine non-dimensional parameters in the phenomenon shown on the right (surface tension of a soap bubble). The variables involved are: R AP - pressure difference between the inside and outside R- radius of the bubble Pide Soap film surface tension (Gravity is not relevant since the soap bubble is neutrally buoyant in air)
How can I use dimensional analysis to show that in this problem both Froude's number and Reynold's number are relevant dimensionless parameters? Problem: Here shallow waves move at speed c. The surface of the waves is a function depth (h), gravitational accelaration is g, densisty is p and fluid viscosity is μ. I need to get the parameter in the form in the image. Please help :)
Problem 1: The discharge pressure (P) of a centrifugal pump shown below is a function of flow rate (Q), impeller diameter (D), fluid density (p), and impeller angular speed (12). P = f (Q. D, p. 92). Use the Buckingham pi technique to rewrite this function in terms of dimensionless parameters, 1 g (n₂). P= P(Q,D, Dimensions 2) N= 5 Q. P
The viscous torque T produced on a disc rotating in a liquid depends upon the characteristic dimension D, the rotational speed N, the density pand the dynamic viscosity u. a) Show that there are two non-dimensional parameters written as: T and a, PND? b) In order to predict the torque on a disc of 0.5 m of diameter which rotates in oil at 200 rpm, a model is made to a scale of 1/5. The model is rotated in water. Calculate the speed of rotation of the model necessary to simulate the rotation of the real disc. c) When the model is tested at 18.75 rpm, the torque was 0.02 N.m. Predict the torque on the full size disc at 200 rpm. Notes: For the oil: the density is 750kg/m² and the dynamic viscosity is 0.2 N.s/m². For water: the density is 1000 kg/ m² and the dynamic viscosity is 0.001 N.s/m². kg.m IN =1
Please solve this problem, Thank you very much! Figure is attached 1. liquids in rotating cylinders rotates as a rigid body and considered at rest. The elevation difference h between the center of the liquid surface and the rim of the liquid surface is a function of angular velocity ?, fluid density ?, gravitational acceleration ?, and radius ?. Use the method of repeating variables to find a dimensionless relationship between the parameters. Show all the steps.
When a liquid in a beaker is stired, whirlpool will form and there will be an elevation difference h, between the center of the liquid surface and the rim of the liquid surface. Apply the method of repeating variables to generate a dimensional relationship for elevation difference (h), angular velocity (@) of the whirlpool, fluid density (p). gravitational acceleration (2), and radius (R) of the container. Take o. pand R as the repeating variables.
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
Question 3 The power, P, to drive an axial pump is in a function of density of fluid, p, volumetric flow rate, Q, pump head, h, diameter of rotor, D, and angular speed of rotor, N. (a) (b) (c) P PDS N3 Verify that - is a dimensionless group. Determine the remaining pi group and perform dimensional analysis. Define geometric similarity and dynamic similarity. Categorize the pi group obtained from part (b) as geometric similarity or dynamic similarity, respectively.