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The absolute pressure inside a liquid jet is slightly greater than the atmospheric pressure. This excess pressure (p), the surface tension (σ) of the liquid and diameter (d) of jet are related as
- a)σ / d
- b)2σ / d
- c)4σ / d
- d)8σ / d
Correct answer is option 'B'. Can you explain this answer?
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The absolute pressure inside a liquid jet is slightly greater than th...
Cut the liquid jet into two halves and consider FBD of one half
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⇒ p × (Ld) = σ × 2L
⇒ p = 2σ / d
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The absolute pressure inside a liquid jet is slightly greater than th...
Cut the liquid jet into two halves and consider FBD of one half
⇒ p × (Ld) = σ × 2L
⇒ p = 2σ / d
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The absolute pressure inside a liquid jet is slightly greater than th...
Understanding Jet Pressure and Surface Tension
The relationship between excess pressure (p), surface tension (σ), and the diameter (d) of a liquid jet is crucial in fluid mechanics. Here's how these parameters are interlinked:
Excess Pressure in Liquid Jets
- The excess pressure (p) inside a liquid jet is a result of the surface tension acting along the curved liquid surface.
- This pressure difference is necessary to balance the forces due to surface tension, ensuring the stability of the jet.
Surface Tension (σ)
- Surface tension is a property of liquids that causes the surface to behave like a stretched elastic membrane.
- It plays a vital role in determining the shape and stability of liquid jets, especially when they are in motion.
Jet Diameter (d)
- The diameter of the jet (d) affects how the liquid interacts with the surrounding air and the forces acting on it.
- A smaller diameter results in a sharper curvature of the liquid surface, leading to a higher impact of surface tension.
Relationship Between p, σ, and d
- The equation relating these three parameters is derived from balancing the forces related to the surface tension and the pressure difference.
- It can be expressed as: p = 2σ/d.
Correct Option and Explanation
- Based on this relationship, the correct answer is option 'B': 2σ/d.
- This indicates that the excess pressure inside the liquid jet is directly proportional to the surface tension and inversely proportional to the diameter of the jet.
This insight is fundamental for understanding fluid behavior in various engineering applications, including nozzle designs and spray mechanisms.
The relationship between excess pressure (p), surface tension (σ), and the diameter (d) of a liquid jet is crucial in fluid mechanics. Here's how these parameters are interlinked:
Excess Pressure in Liquid Jets
- The excess pressure (p) inside a liquid jet is a result of the surface tension acting along the curved liquid surface.
- This pressure difference is necessary to balance the forces due to surface tension, ensuring the stability of the jet.
Surface Tension (σ)
- Surface tension is a property of liquids that causes the surface to behave like a stretched elastic membrane.
- It plays a vital role in determining the shape and stability of liquid jets, especially when they are in motion.
Jet Diameter (d)
- The diameter of the jet (d) affects how the liquid interacts with the surrounding air and the forces acting on it.
- A smaller diameter results in a sharper curvature of the liquid surface, leading to a higher impact of surface tension.
Relationship Between p, σ, and d
- The equation relating these three parameters is derived from balancing the forces related to the surface tension and the pressure difference.
- It can be expressed as: p = 2σ/d.
Correct Option and Explanation
- Based on this relationship, the correct answer is option 'B': 2σ/d.
- This indicates that the excess pressure inside the liquid jet is directly proportional to the surface tension and inversely proportional to the diameter of the jet.
This insight is fundamental for understanding fluid behavior in various engineering applications, including nozzle designs and spray mechanisms.
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The absolute pressure inside a liquid jet is slightly greater than the atmospheric pressure. This excess pressure (p), the surface tension (σ) of the liquid and diameter (d) of jet are related asa) σ / db) 2σ / dc) 4σ / dd) 8σ / dCorrect answer is option 'B'. Can you explain this answer?
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