Calculating Hydrostatic and Gravitational Forces in Fluid Mechanics

[Forceflow]

In Figure 14-31, an open tube of length L = 1.8 m and cross-sectional area A = 4.6 cm2 is fixed to the top of a cylindrical barrel of diameter D = 1.2 m and height H = 1.8 m. The barrel and tube are filled with water (to the top of the tube). Calculate the ratio of the hydrostatic force on the bottom of the barrel to the gravitational force on the water contained in the barrel.
Why is that ratio not equal to 1.0? (You need not consider the atmospheric pressure.)

I calculated the ratio and the ratio is 2. However, i have no clue to why that ratio wouldn't be equal to one.

 

[Andrew Mason]

In Figure 14-31, an open tube of length L = 1.8 m and cross-sectional area A = 4.6 cm2 is fixed to the top of a cylindrical barrel of diameter D = 1.2 m and height H = 1.8 m. The barrel and tube are filled with water (to the top of the tube). Calculate the ratio of the hydrostatic force on the bottom of the barrel to the gravitational force on the water contained in the barrel.
Why is that ratio not equal to 1.0? (You need not consider the atmospheric pressure.)

I calculated the ratio and the ratio is 2. However, i have no clue to why that ratio wouldn't be equal to one.

Why not show us what you did.

The gravitational force on the water contained in the barrel is the weight of the water in the barrel, which is equal to its mass x gravitational acceleration: Mg.

The hydrostatic force on the bottom of the barrel is equal to the weight of the water above it: weight of water in both tube and barrel.

So the ratio is M/(M+m) where M is the mass of the barrel and m is the mass of the water in the tube. That should be 100/(100+1)

AM

 

[kyle8921]

I can explain why the ratio of hydrostatic force to gravitational force is not equal to 1.0 in this scenario.

Firstly, let's understand the concepts of hydrostatic force and gravitational force. Hydrostatic force is the force exerted by a fluid on an object submerged in it, while gravitational force is the force of gravity acting on the same object.

In this case, the hydrostatic force on the bottom of the barrel is equal to the weight of the water column above it, which is calculated by multiplying the density of water (1000 kg/m3) by the height of the water column (1.8 m) and the cross-sectional area of the barrel (πr2). On the other hand, the gravitational force on the water contained in the barrel is calculated by multiplying the mass of the water (density x volume) by the acceleration due to gravity (9.8 m/s2).

Now, the reason why the ratio of these two forces is not equal to 1.0 is because the hydrostatic force is only acting on the bottom of the barrel, while the gravitational force is acting on the entire volume of water in the barrel. This means that the gravitational force is acting on a larger area compared to the hydrostatic force, resulting in a larger force.

In addition, the shape of the barrel and the tube also play a role in this ratio. The barrel has a larger diameter compared to the tube, meaning that the weight of the water in the barrel is distributed over a larger area, resulting in a smaller hydrostatic force on the bottom of the barrel.

Furthermore, the height of the water column in the tube is limited by the height of the barrel, while the gravitational force is acting on the entire volume of water in the barrel. This also contributes to the difference in the ratio.

In conclusion, the ratio of hydrostatic force to gravitational force is not equal to 1.0 because of the differences in the distribution of forces and the shape of the container. This is a common phenomenon in fluid mechanics and can be observed in various scenarios.