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MM + 2,5 t.

MM + 2,5 t.

Structural Analysis
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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Fluids mechanics 

Assuming head loss derive Bernoulli equation

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The image contains a series of fluid dynamics equations and a diagram of a fluid reservoir. Below is a transcription and explanation suitable for an educational website: **Transcription:** 1. \( \frac{P_1}{\gamma} + \frac{V_1^2}{2g} + Z_1 = \frac{P_2}{\gamma} + \frac{V_2^2}{2g} + Z_2 + \frac{fL}{D} \frac{V^2}{2g} + K_L \frac{V_2^2}{2g} \) 2. \( \frac{V_1}{V_2} \leq \left( \frac{P_2}{P_1} \right)^2 \Rightarrow V_5 \) 3. \( V_2 \leq \left( \frac{P_2}{D_1} \right)^2 \) 4. \( V_2 \leq \sqrt{\frac{2gh}{1 + kL}} \) **Diagram Explanation:** - The diagram on the left side represents a fluid reservoir with a vertical pipe. The reservoir indicates different levels, suggesting measurements of fluid height and velocity head. - The equations likely derive from Bernoulli’s equation, which is fundamental in fluid dynamics to describe the behavior of a fluid moving along a streamline. - The terms within the equations denote: - \( P_1, P_2 \): Pressure at point 1 and point 2 - \( \gamma \): Specific weight of the fluid - \( V_1, V_2 \): Velocity of the fluid at point 1 and point 2 - \( Z_1, Z_2 \): Elevation head at point 1 and point 2 - \( f \): Friction factor - \( L/D \): Length-to-diameter ratio of the pipe - \( K_L \): Loss coefficient - \( g \): Acceleration due to gravity (approximately 9.81 m/s²) - \( h \): Height of the fluid column This analysis provides insights into the energy conservation and loss mechanisms in pipe flow systems. The equations aim to find relationships between fluid velocities, pressure heads, and other factors influencing fluid flow in pipes.
Transcribed Image Text:The image contains a series of fluid dynamics equations and a diagram of a fluid reservoir. Below is a transcription and explanation suitable for an educational website: **Transcription:** 1. \( \frac{P_1}{\gamma} + \frac{V_1^2}{2g} + Z_1 = \frac{P_2}{\gamma} + \frac{V_2^2}{2g} + Z_2 + \frac{fL}{D} \frac{V^2}{2g} + K_L \frac{V_2^2}{2g} \) 2. \( \frac{V_1}{V_2} \leq \left( \frac{P_2}{P_1} \right)^2 \Rightarrow V_5 \) 3. \( V_2 \leq \left( \frac{P_2}{D_1} \right)^2 \) 4. \( V_2 \leq \sqrt{\frac{2gh}{1 + kL}} \) **Diagram Explanation:** - The diagram on the left side represents a fluid reservoir with a vertical pipe. The reservoir indicates different levels, suggesting measurements of fluid height and velocity head. - The equations likely derive from Bernoulli’s equation, which is fundamental in fluid dynamics to describe the behavior of a fluid moving along a streamline. - The terms within the equations denote: - \( P_1, P_2 \): Pressure at point 1 and point 2 - \( \gamma \): Specific weight of the fluid - \( V_1, V_2 \): Velocity of the fluid at point 1 and point 2 - \( Z_1, Z_2 \): Elevation head at point 1 and point 2 - \( f \): Friction factor - \( L/D \): Length-to-diameter ratio of the pipe - \( K_L \): Loss coefficient - \( g \): Acceleration due to gravity (approximately 9.81 m/s²) - \( h \): Height of the fluid column This analysis provides insights into the energy conservation and loss mechanisms in pipe flow systems. The equations aim to find relationships between fluid velocities, pressure heads, and other factors influencing fluid flow in pipes.
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