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The equation for hydrostatic pressure is given by P = rgh, where P represents the hydrostatic pressure, r is the fluid density, g is the acceleration due to gravity, and h is the height of the fluid column above the point in question.
This equation is derived from the principle that fluids at rest exert pressure uniformly in all directions. When considering a column of liquid, the pressure at any depth is due to the weight of the liquid above that point. As depth increases (increasing the height, h), the pressure experienced at that point increases proportionally to the density of the fluid and the gravitational pull acting on it.
The other equations provided correspond to different physical concepts. For instance, the equation P = nRT is the ideal gas law, which relates the pressure of a gas to its amount, temperature, and volume. Similarly, P = I * R pertains to electrical circuits, describing the relationship between current, voltage, and resistance. Finally, P = 1/2kx^2 describes the potential energy stored in a spring, known as Hooke's Law. Each of these equations is fundamental in their respective fields but does not relate to the calculation of hydrostatic pressure in a fluid.