Obtain Bernoulli's equation for a fluid at rest.

(N/A) Bernoulli's equation is given by:
$P_{1} + \frac{1}{2} \rho v_{1}^{2} + \rho g h_{1} = P_{2} + \frac{1}{2} \rho v_{2}^{2} + \rho g h_{2}$
When a fluid is at rest,its velocity at every point is zero. Therefore,we substitute $v_{1} = 0$ and $v_{2} = 0$ into the equation:
$P_{1} + \rho g h_{1} = P_{2} + \rho g h_{2}$
Rearranging the terms,we get:
$P_{1} - P_{2} = \rho g(h_{2} - h_{1})$
This represents the hydrostatic pressure variation in a fluid at rest.