A closed, 5 -m-tall tank is filled with water to a depth of 4 m The top portion of the tank is f

step 1 To solve this problem first I will just write the given data here. So here the value of p1 is eq

A closed, 5 -m-tall tank is filled with water to a depth of...

A closed, 5 -m-tall tank is filled with water to a depth of $4 \mathrm{m}$ The top portion of the tank is filled with air which, as indicated by a pressure gage at the top of the tank, is at a pressure of $20 \mathrm{kPa}$. Determine the pressure that the water exerts on the bottom of the $\operatorname{tank}$.

Key Concepts

Hydrostatic Pressure

Hydrostatic pressure refers to the pressure exerted by a fluid at rest due to the force of gravity. It increases linearly with depth, and it is calculated using the product of the fluid’s density, gravitational acceleration, and the height of the fluid column over the point of interest. This concept is fundamental in understanding how pressure varies with depth in any static fluid situation.

Gauge Pressure

Gauge pressure is the pressure measured relative to the ambient atmospheric pressure. In many practical applications, instruments are calibrated as pressure gages that provide the difference between the absolute pressure and the atmospheric pressure. This concept is essential when dealing with closed systems or when comparing the internal pressures with a reference pressure level.

Pressure Variation with Depth

The pressure in a static fluid increases with depth because each additional layer of fluid adds to the weight exerting force on the layers below. The pressure difference between two points in a fluid is determined solely by the weight of the fluid between them. This relationship is critical in analyzing problems involving fluid columns and interfaces between fluids and gases.

Boundary Conditions in Fluid Statics

When analyzing the pressure at a point within a fluid, especially in enclosed or partially enclosed systems, it is important to consider the boundary conditions such as the pressure at the fluid’s surface. In cases where the exposed fluid interface is subject to an external pressure different from atmospheric pressure, this boundary condition directly influences the pressures calculated at points within the fluid.

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