Problem 5: Dimensional AnalysisUse the Buckingham Pi Theorem (Song, 2018, pages 219-221) to derive an equation for frictionhead loss, hr, as a function of gravitational acceleration, g, pipe diameter, D, pipe length, L, andaverage velocity, V=QIA.Step 1-List the dimensional parameters (N, ni, n2, ...).Step 2-List the dimensions of all parameters in terms of primary dimensions.Step 3-Select a set of primary dimensions (MLT or FLT).Step 4-Select a set of repeating parameters.Step 5-Set up one or more dimensional equations in the form N= n*n2n3², then solve for theunknown exponents.

Gravitational accelerationPipe diameterPipe lengthAverage velocityTo find: Equation for friction…

Problem 5: Dimensional Analysis Use the Buckingham Pi Theorem (Song, 2018, pages 219-221) to derive an equation for friction head loss, hr, as a function of gravitational acceleration, g, pipe diameter, D, pipe length, L, and average velocity, V=Q/A. Step 1-List the dimensional parameters (N, n₁, n₂, ...). Step 2-List the dimensions of all parameters in terms of primary dimensions. Step 3-Select a set of primary dimensions (MLT or FLT). Step 4-Select a set of repeating parameters. Step 5-Set up one or more dimensional equations in the form N= n*n2n3², then solve for the unknown exponents.

Problem 5: Dimensional Analysis Use the Buckingham Pi Theorem (Song, 2018, pages 219-221) to derive an equation for friction head loss, hr, as a function of gravitational acceleration, g, pipe diameter, D, pipe length, L, and average velocity, V=Q/A. Step 1-List the dimensional parameters (N, n₁, n₂, ...). Step 2-List the dimensions of all parameters in terms of primary dimensions. Step 3-Select a set of primary dimensions (MLT or FLT). Step 4-Select a set of repeating parameters. Step 5-Set up one or more dimensional equations in the form N= n*n2n3², then solve for the unknown exponents.

Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)

5th Edition

ISBN:9781305084766

Author:Saeed Moaveni

Publisher:Saeed Moaveni

Chapter6: Fundamental Dimensions And Units

Section: Chapter Questions

Problem 49P

See similar textbooks

Similar questions

Given the acceleration-time diagram sketch the velocity-time diagram and determine the displacement at time=9s.
Assign the values of shear force and bending moment to the image beam as a function of the x coordinate. q = 22 kN / m, F = 14 kN, M = 10 kNm L1 = 1.2 m, L2 = 1.9 m, L3 = 1.2 m, L4 = 1.9 m Use units [kN, m] Enter your answers to three decimal places. Do not round off the invoices in the intermediate stages, but only the final answer!
Instruction: Read the problems carefully and provide complete solutions with derivation of formulas (integrals and derivatives). If not stated, the gravitational constant is ? = 9.81 ?/?^2. Note: Make your solution readable.
The plane shaded area given in the figure;a) Find the coordinates of the center of gravity (xG, yG) for the given axis set. (r2 = 5cm and the coordinates of the A point are A (15; 10) cm.)b) Calculate the volume of the object obtained by rotating the shaded area around the x-axis by 3600 using the Pappus-Guldinus theorem.v
Determine the slope and vertical displacement of point A on the beam shown in the accompanying illustration. Use Conjugate Beam Method. E = 200,000 MPa
Limitations on the Use of the Bernoulli Equation A two dimensional flow field is given by u=2y, v=x. (a) sketch the flow field. (b)Derive a general expression for the velocity and acceleration(x and y are in units of length L; u and v are in units of L/T). (c) Find the acceleration in the flow field at point A (x=3.5, y=1.2).
Show the complete solution and the necessary graphs/diagrams. Use 2 decimal places in the final answer. The rotation of the 0.9-m arm OA about O is defined by the relation Eq. (1), where θ is expressed in radians and t in seconds. Collar B slides along the arm in such a way that its distance from O is Eq. (2), where r is expressed in meters and t in seconds. After the arm OA has rotated through 30°, determine the velocity of the collar (m/s).
Show the complete solution and the necessary graphs/diagrams. Use 2 decimal places in the final answer. The rotation of the 0.9-m arm OA about O is defined by the relation Eq. (1), where θ is expressed in radians and t in seconds. Collar B slides along the arm in such a way that its distance from O is Eq. (2), where r is expressed in meters and t in seconds. After the arm OA has rotated through 30°, determine the relative acceleration of the collar with respect to the arm (m/s^2).
Show the complete solution and the necessary graphs/diagrams. Use 2 decimal places in the final answer. The rotation of the 0.9-m arm OA about O is defined by the relation Eq. (1), where θ is expressed in radians and t in seconds. Collar B slides along the arm in such a way that its distance from O is Eq. (2), where r is expressed in meters and t in seconds. After the arm OA has rotated through 30°, determine the acceleration of the collar (m/s^2).
The below container in which there are two immiscible fluids. Plot the pressure distribution, that is, draw the chart for vs. (from the bottom to the top). Use the chart type scatter with straight lines and markers. z values should increase by 1 m. Name your axes including the units in parentheses.
I don't understand problem 9.12 from fox and Mcdonalds introduction to fluid mechanics 9th edition. We are to evalutate the displacement thickness delta* and the momentum thickness theta for a power law velocity profile given by u/U = (y/delta)^1/7 thanks
Derive the expression for variations of pressure with the location in fluid at rest using a wedge-shaped elementary area. Consider downward going vertical axis as the positive direction