# Another Hydrostaic force Problem

In summary, the conversation revolves around a problem from a calculus book which involves finding the hydrostatic force on one end of a cylindrical drum submerged in water. The participants discuss the definition of pressure and the calculations involved in finding the pressure at different points on the drum. It is noted that the book makes an error by neglecting to account for gravitational acceleration.
This is a problem right out of the text of my calculus book. So I actually have the work, but I'm confused about something the did.

Problem: Find the hydrostatic force on one end of a cylindrical drum with radius 3 ft. if the drum is submerged in water 10 ft deep.

I attached a diagram

Pressure can be defined:

p=density, d=distance below the surface

$$P=pgd=\delta d$$

The area of the ith strip is:

$$A_i=2\sqrt{9-(y^*_i)^2}\Delta y$$

The average distance below the surface is:

$$d_i=7-y^*_i$$

Then when they write the pressure, they give:

$$\delta_i=62.5(7-y^*_i)$$

The implies that $$pg=62.5$$.

The density of water is $$p=62.4 lb/ft^3$$

http://en.wikipedia.org/wiki/Density_of_water

Gravitational acceleration is $$32.174 ft/s^2$$

So how does $$\delta d_i=pgd_i=62.5(7-y^*_i)$$ ? Is this an error? It seems that they accidently neglected to account for gravitational acceleration.

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Yeah, it's an error.

Hello,

Thank you for bringing this to my attention. It does seem that there may be an error in the given solution. The correct expression for pressure in this problem should be P = ρgd, where ρ is the density of water, g is the gravitational acceleration, and d is the distance below the surface. In this case, the correct value for ρ is indeed 62.4 lb/ft^3 and the correct value for g is 32.174 ft/s^2. Therefore, the correct expression for pressure should be P = (62.4 lb/ft^3)(32.174 ft/s^2)(7-y*_i).

I suggest double checking your calculations and possibly consulting with your instructor or a classmate to confirm the correct solution. It is important to make sure all units are consistent and accounted for in order to obtain an accurate result.

I hope this helps clarify the confusion. Let me know if you have any further questions or concerns. Keep up the good work in your calculus studies!

## What is hydrostatic force?

Hydrostatic force is the force exerted by a fluid on an object that is submerged or partially submerged in the fluid.

## What factors affect the magnitude of hydrostatic force?

The magnitude of hydrostatic force is affected by the density of the fluid, the depth of the object in the fluid, and the gravitational acceleration.

## How is hydrostatic force calculated?

Hydrostatic force is calculated using the formula F = ρghA, where ρ is the density of the fluid, g is the gravitational acceleration, h is the depth of the object in the fluid, and A is the area of the object.

## What are some real-world applications of hydrostatic force?

Hydrostatic force is used in a variety of fields, including engineering, architecture, and hydrology. It is essential in designing structures such as dams, bridges, and ships, and in understanding the movement of fluids in natural systems.

## What is the difference between hydrostatic pressure and hydrostatic force?

Hydrostatic pressure refers to the pressure exerted by a fluid at a certain depth, while hydrostatic force is the total force exerted by the fluid on an object. Hydrostatic force takes into account both the pressure and the area of the object, while hydrostatic pressure only considers the pressure.

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