Pressure at c in example problem no 1 in this page fluid statics??

To determine the pressure at point C in a fluid statics problem, we need to consider the principles of hydrostatics, which govern how fluids behave at rest. The pressure at a specific point in a fluid is influenced by the height of the fluid column above that point, as well as the density of the fluid. Let’s break this down step by step.

Understanding Fluid Pressure

In fluid statics, the pressure at a given depth in a fluid is given by the equation:

P = P₀ + ρgh

• P = pressure at depth
• P₀ = atmospheric pressure (or pressure at the surface)
• ρ = density of the fluid
• g = acceleration due to gravity (approximately 9.81 m/s²)
• h = height of the fluid column above the point

Applying the Formula

To find the pressure at point C, we first need to identify the height of the fluid column above point C. Let’s say, for example, that point C is located at a depth of 5 meters in a water column. The density of water is approximately 1000 kg/m³.

Using the formula, we can substitute the values:

P = P₀ + (1000 kg/m³)(9.81 m/s²)(5 m)

Calculating the Pressure

Assuming atmospheric pressure (P₀) is about 101,325 Pa (or 101.3 kPa), we can calculate:

P = 101325 Pa + (1000)(9.81)(5)

P = 101325 Pa + 49050 Pa

P = 150375 Pa

Interpreting the Result

The pressure at point C, therefore, would be 150,375 Pa, or 150.4 kPa. This value indicates the total pressure exerted at that depth, combining both the atmospheric pressure and the pressure due to the water column above it.

Visualizing the Concept

Think of it like stacking books on a table. The weight of the books (analogous to the water column) adds pressure to the table (the point where we measure pressure). The deeper you go, the more books (or water) are stacked above, increasing the pressure you feel at the bottom.

In summary, to find the pressure at point C, you need to know the height of the fluid above it and the fluid's density. By applying the hydrostatic pressure formula, you can easily calculate the pressure at any point in a fluid at rest.