**Problem 5: Dimensional Analysis**Use the Buckingham Pi Theorem (Song, 2018, pages 219-221) to derive an equation for friction head loss, \( h_r \), 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 \((N, n_1, n_2, \ldots)\).**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 \( N = \Pi n_1^{x_1}n_2^{x_2}n_3^{x_3} \), then solve for the unknown 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.

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Concept explainers

Laws of Equilibrium

A body is said to be in equilibrium if the system of forces acting on the body tends to keep the body at rest, in other words, there is no translation motion or net torque on the body. Under such conditions, the equilibrium conditions are to be applied to analyze the condition. The branch of mechanics that deals with this condition is known as 'statics'. Under equilibrium, there are no net forces on the body.

Question

**Problem 5: Dimensional Analysis**

Use the Buckingham Pi Theorem (Song, 2018, pages 219-221) to derive an equation for friction head loss, \( h_r \), 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 \((N, n_1, n_2, \ldots)\).

**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 \( N = \Pi n_1^{x_1}n_2^{x_2}n_3^{x_3} \), then solve for the unknown exponents.

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Step 2: Determine the number of Pi terms.

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