Which expression represents Bernoulli's equation for incompressible flow along a streamline?

Which expression represents Bernoulli's equation for incompressible flow along a streamline?

• A. p/ρg + v^2/(2g) - z = constant
• B. p/ρg + v^2/g + z = constant
• C. p/ρg - v^2/(2g) + z = constant
• D. p/ρg + v^2/(2g) + z = constant

Answer: (D)

Bernoulli's principle for steady, incompressible flow along a streamline says the total energy per unit weight stays constant as a fluid particle moves. Expressed in common form, this is p/(ρ g) + v^2/(2 g) + z = constant. Here the terms have clear meanings: p/(ρ g) is the pressure head, v^2/(2 g) is the velocity head (kinetic energy per unit weight), and z is the elevation head (gravitational potential energy per unit weight). The sum remains constant along a streamline, so the correct expression combines these three heads with plus signs. If you see a form with v^2/g, that would double the velocity head, which isn’t consistent with energy balance. If z were negative, it would imply energy decreases with elevation, which contradicts the standard convention for potential energy per unit weight.

Bernoulli's principle for steady, incompressible flow along a streamline says the total energy per unit weight stays constant as a fluid particle moves. Expressed in common form, this is p/(ρ g) + v^2/(2 g) + z = constant. Here the terms have clear meanings: p/(ρ g) is the pressure head, v^2/(2 g) is the velocity head (kinetic energy per unit weight), and z is the elevation head (gravitational potential energy per unit weight). The sum remains constant along a streamline, so the correct expression combines these three heads with plus signs.

If you see a form with v^2/g, that would double the velocity head, which isn’t consistent with energy balance. If z were negative, it would imply energy decreases with elevation, which contradicts the standard convention for potential energy per unit weight.