Fluids mechanics Assuming head loss derive Bernoulli equationto the resulted answer 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 columnThis 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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Civil Engineering

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Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

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Problem 1P

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Concept explainers

Time and time related variables in engineering

Time is the event progression starting from past to present and then, future statistically. The time-related variable is any particular value in relation to time to assess its changes on a specified (XY) plane.

Question

Fluids mechanics

Assuming head loss derive Bernoulli equation

to the resulted answer

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.

Branch of science that deals with the stationary and moving bodies under the influence of forces.

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