Which of the following represents the formula for total force?

The formula for total force relates to the calculation of pressure applied over an area. In this context, it is essential to identify the area over which the force is distributed. The area of a circular cross-section can be calculated using the formula for the area of a circle, which is ( A = \pi r^2 ). Alternatively, when considering the diameter ( D ), the area can also be represented as:

[

A = \frac{\pi}{4} D^2

]

This accounts for the full area when substituting the diameter into the area formula. The numerical value ( 0.7854 ) is the simplified representation of ( \frac{\pi}{4} ) and indicates that when force is calculated over a circular area, this factor is necessary to obtain accurate results.

Thus, the total force can be expressed as the product of this area and pressure:

[

\text{Total Force} = A \times \text{Pressure} = \left(\frac{\pi}{4} D^2\right) \times \text{Pressure}

]

This aligns perfectly with option B, confirming that it correctly incorporates the factor for the area of a circle in terms of diameter while considering the