How does a decrease in the cross-sectional area of a pipe affect fluid flow?

A decrease in the cross-sectional area of a pipe results in an increase in fluid velocity and a decrease in pressure. This phenomenon can be explained using the principle of continuity and Bernoulli's equation.

According to the principle of continuity, the product of the cross-sectional area of a pipe and the fluid velocity must remain constant if the fluid is incompressible and there are no leaks. Therefore, when the cross-sectional area decreases, the velocity of the fluid must increase to maintain the same flow rate. This is similar to how squeezing a hose causes the water to shoot out faster.

Additionally, Bernoulli's equation states that an increase in the velocity of a fluid results in a corresponding decrease in pressure. This relationship occurs because the total mechanical energy in a flow must remain constant; hence, when kinetic energy (which is related to velocity) increases, the potential energy (which is associated with pressure) must decrease.

These principles work together to explain how a smaller cross-sectional area leads to a higher fluid velocity and lower pressure within the pipe.