Derivation On Sudden Closure Of Valve When Pipe Is Elastic - Pipe Network and Water Hammer Effect | Summary and Q&A

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April 4, 2022
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Derivation On Sudden Closure Of Valve When Pipe Is Elastic - Pipe Network and Water Hammer Effect

TL;DR

This video explains the derivation for the pressure increase in an elastic pipe material and the factors that contribute to strain energy stored in the pipe walls.

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Key Insights

  • 😚 Elasticity in pipe materials can affect the pressure increase when a pipe is suddenly closed.
  • 🏪 Strain energy is stored in the walls of elastic pipes due to longitudinal and circumferential stresses.
  • ❓ The strain energy in pipe materials can be calculated using formulas involving pressure, diameter, thickness, length, and elasticity.
  • 😵 The strain energy in water can also be calculated using formulas involving density, cross-sectional area, length, velocity, and compressibility.
  • 💦 The gain in strain energy in water is equal to the loss in kinetic energy of water plus the strain energy stored in the pipe.

Questions & Answers

Q: What is the significance of considering elasticity in pipes made of elastic materials?

Pipes made of elastic materials store some energy in their elasticity, which affects the pressure increase when the pipe is suddenly closed. Understanding this elasticity is important for various engineering applications, such as pipe design and calculation of pressure changes.

Q: How is strain energy calculated in pipe materials?

The strain energy in pipe materials can be calculated using the formula: Strain energy = 1/2 * (P^2 * A * D * L) / (8 * e^2), where P is the pressure, A is the cross-sectional area of the pipe, D is the diameter, L is the length, and e is the elasticity of the material.

Q: What is the formula for circumferential and longitudinal stresses in pipe materials?

The formula for circumferential stress is Sigma C = P * D / (2 * T), and the formula for longitudinal stress is Sigma L = P * D / (4 * T), where P is the pressure and D is the diameter of the pipe. T is the thickness of the pipe wall.

Q: How does the strain energy in water relate to the strain energy in the pipe material?

The strain energy in water can be calculated using the formula: Strain energy in water = 1/2 * (Rho * A * L * V^2) / K, where Rho is the density of water, A is the cross-sectional area of the pipe, L is the length, V is the velocity of water, and K is a factor related to the compressibility of water. The strain energy in water and the pipe material are related through the equation: Loss in kinetic energy of water = Gain in kinetic energy of water + Strain energy stored in the pipe.

Summary & Key Takeaways

  • The video discusses the concepts of strain energy and elasticity in pipes made of elastic materials.

  • It explains the longitudinal and circumferential stresses generated in the pipe walls due to pressure.

  • The video provides the formula for the total strain energy in the pipe material and explains the relation between strain energy in water and the pipe.

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