Why pressure is inversely proportional to velocity in bernoulli's equation?

Answer 1

Usually in a streamlined motion the sum of three heads have to be constant always.

They are

pressure head

velocity head and

gravitational head

In case of horizontal pipe gravitational head is already a constant

Now velocity head + pressure head = constant

So as velocity head increases then automatically pressure head has to fall.

Answer 2

In Bernoulli's equation, pressure is inversely proportional to velocity because of the conservation of energy principle. When the fluid speed increases, its kinetic energy increases at the expense of its pressure energy, and vice versa. This relationship between pressure and velocity ensures that total mechanical energy along a streamline remains constant in an ideal fluid flow.