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Chapter 4: Problem 31

What important thing happens when the speed of a moving fluid increases?

Short Answer

Expert verified
Answer: When the speed of a moving fluid increases, the pressure within the fluid decreases. This phenomenon is explained by Bernoulli's Equation, which is based on the conservation of energy in fluid dynamics.

Step by step solution

01

Bernoulli's Equation

Bernoulli's Equation is a fundamental principle in fluid dynamics that describes the behavior of a moving fluid. It states that for an incompressible fluid, the sum of its pressure (P), kinetic energy per unit volume (1/2 * density * velocity^2), and potential energy per unit volume (density * gravitational acceleration * height) remains constant along a streamline. The equation is written as: $$ P + \frac{1}{2} \rho v^2 + \rho gh = constant $$
02

Increasing Fluid Speed

According to Bernoulli's Equation, as the speed of a moving fluid increases, its kinetic energy per unit volume increases as well. This increase in kinetic energy results in some important consequences for the fluid's pressure and potential energy per unit volume.
03

Relationship between Fluid Speed and Pressure

As the fluid's velocity (speed) increases, the kinetic energy term (1/2 * density * velocity^2) becomes larger. Due to the conservation of energy principle, this increase in kinetic energy must be compensated by a decrease in pressure and/or potential energy per unit volume. In situations where the change in height is negligible, we can simplify the equation to: $$ P + \frac{1}{2} \rho v^2 = constant $$ Now it's more apparent that an increase in fluid speed (velocity) will result in a decrease in pressure.
04

Conclusion

So, the important thing that happens when the speed of a moving fluid increases is that the pressure within the fluid decreases. This phenomenon is in accordance with Bernoulli's Equation and the conservation of energy in fluid dynamics.

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