Water is flowing through a pipe under constant pressure. At some place the pipe becomes narrow. The pressure of water at this place:
Step 1: Concept used
Principle of continuity:
According to the principle of continuity, if the fluid is in streamlined flow and is in-compressible then we can say that mass of fluid passing through different cross-sections are equal.
Where, and are the areas of cross-section, and and are the flow velocities at two different points as shown in the figure below.
According to Bernoulli's theorem:
Here, is the pressure exerted by the fluid, is the density of the fluid, is the velocity of the fluid, is the height of the container.
Step 2: Explanation
From the above equation, it is clear that if velocity is increasing then the pressure will decrease.
Hence, the pressure of water in narrow places will decrease.