Euler's equation of motion for inviscid flow: differential form Select the correct differential relation along a streamline for steady, frictionless flow of a fluid of density ρ.
Mechanical Engineering
Hydraulics and Fluid Mechanics
Difficulty: Medium
Choose an option
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Adp + ρ V dV + ρ g dz = 0
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Bdp/ρ + V dV + g dz = 0
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Cdp/ρ − V dV + g dz = 0
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Ddp/ρ + V dV − g dz = 0
Answer
Correct Answer: dp/ρ + V dV + g dz = 0
Explanation
Concept/Approach
- Euler's equation (along a streamline, inviscid): the sum of differential pressure head, velocity head and elevation head changes is zero.
Statementdp/ρ + V dV + g dz = 0Integrating gives Bernoulli's relation: p/ρ + V²/2 + g z = constant.
Final Answerdp/ρ + V dV + g dz = 0