Fluid Flow: Water flows through a pipe. The diameter of the pipe at point B is larger than at point A. Where is the water pressure greatest?

The water pressure is greatest at point A. This is due to the principle of fluid dynamics known as Bernoulli's Principle, which states that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy.

Here are the steps to understand this:

1. When water flows from point A to point B, it moves from a region of smaller cross-sectional area to a region of larger cross-sectional area.

2. According to the principle of continuity, which states that the mass flow rate must remain constant in a pipe, the velocity of the water decreases as it moves from point A to point B. This is because the flow rate (which is the product of the cross-sectional area of the pipe and the velocity of the fluid) must remain constant. So, if the area increases, the velocity must decrease to keep the flow rate constant.

3. According to Bernoulli's principle, when the velocity of a fluid decreases, its pressure increases. Therefore, the pressure of the water is greater at point A where the velocity of the water is higher.

So, the water pressure is greatest at point A where the pipe is narrower.