Question:
In which of the following condition(s), Bernoulli's equation is applicable?
In which of the following condition(s), Bernoulli's equation is applicable?
Show Hint
Bernoulli's equation assumes steady, incompressible, inviscid flow applied along a single streamline; unsteady flow invalidates the standard form.
Updated On: Jul 17, 2026
- incompressible flow.
- inviscid flow.
- unsteady flow.
- flow along a streamline.
Show Solution
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The Correct Option is A, B, D
Solution and Explanation
Step 1: Recall the derivation assumptions of Bernoulli's equation.
P/rho + v^2/2 + gz = constant is derived by integrating the Euler equation along a streamline, assuming steady, incompressible, inviscid flow.
Step 2: Option A - incompressible.
The pressure integral dP/rho only reduces to P/rho when rho is constant. TRUE.
Step 3: Option B - inviscid.
No viscous dissipation term exists in the equation; friction would need a head-loss term instead. TRUE.
Step 4: Option C - unsteady.
The standard derivation explicitly assumes steady flow (no local acceleration term); unsteady flow invalidates the simple form. FALSE.
Step 5: Option D - along a streamline.
The equation is only valid between two points on the same streamline. TRUE.
Step 6: Conclusion.
A, B, D are conditions for applicability; unsteady flow (C) is excluded, not included. \[ \boxed{A, B, D} \]
P/rho + v^2/2 + gz = constant is derived by integrating the Euler equation along a streamline, assuming steady, incompressible, inviscid flow.
Step 2: Option A - incompressible.
The pressure integral dP/rho only reduces to P/rho when rho is constant. TRUE.
Step 3: Option B - inviscid.
No viscous dissipation term exists in the equation; friction would need a head-loss term instead. TRUE.
Step 4: Option C - unsteady.
The standard derivation explicitly assumes steady flow (no local acceleration term); unsteady flow invalidates the simple form. FALSE.
Step 5: Option D - along a streamline.
The equation is only valid between two points on the same streamline. TRUE.
Step 6: Conclusion.
A, B, D are conditions for applicability; unsteady flow (C) is excluded, not included. \[ \boxed{A, B, D} \]
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