What does Bernoulli's Principle say about velocity and pressure in a flowing fluid?

What does Bernoulli's Principle say about velocity and pressure in a flowing fluid?

• A. As velocity increases, temperature increases.
• B. As velocity increases, density decreases.
• C. As velocity decreases, pressure decreases.
• D. As velocity increases, pressure decreases.

Answer: (D)

In steady, incompressible flow, energy along a streamline is conserved, so the sum of static pressure and dynamic pressure stays constant (P + ½ρv² ≈ constant) when height changes are negligible. That means when the fluid speeds up (v increases), the static pressure (P) must drop to keep the total the same. So faster-moving portions of the fluid have lower pressure. This is why a constricted section speeds up the flow and the pressure there falls, while wider sections move slower and have higher pressure. The statements about temperature or density aren’t the direct relationship described by Bernoulli in this same simple form, so the best-supported takeaway is that velocity up corresponds to pressure down.

In steady, incompressible flow, energy along a streamline is conserved, so the sum of static pressure and dynamic pressure stays constant (P + ½ρv² ≈ constant) when height changes are negligible. That means when the fluid speeds up (v increases), the static pressure (P) must drop to keep the total the same. So faster-moving portions of the fluid have lower pressure. This is why a constricted section speeds up the flow and the pressure there falls, while wider sections move slower and have higher pressure. The statements about temperature or density aren’t the direct relationship described by Bernoulli in this same simple form, so the best-supported takeaway is that velocity up corresponds to pressure down.