- #1

AdkinsJr

- 150

- 0

I need to find the hydrostatic force exerted on a plane submerged vertically in water. I attached a diagram of the problem.

Here are the basic definitions:

---------------------------

d=distance from surface, p=density, P=pressure

[tex]p=\frac{m}{V}[/tex]

[tex]P=pgd=\delta d[/tex]

[tex]F=mg=pgAd[/tex]

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The area of the ith strip is [tex]A_i=6\Delta y[/tex] so the pressure exerted on the ith strip is [tex]\delta d_i=pgd_i=pg(6-y_i^*)[/tex]

The hydrostatic force on the ith strip is [tex]F_i=\delta_iA_i=6pg(6-y_i)\Deltay[/tex]

The approximate force along the entire surface is therefore:

[tex]F_{net}=\lim_{n-\infty}\Sigma_{i=1}^n6pg(6-y_i)\Delta y[/tex]

[tex]=6pg\int_0^4(6-y)dy[/tex]

Am I setting this up correctly?

Here are the basic definitions:

---------------------------

d=distance from surface, p=density, P=pressure

[tex]p=\frac{m}{V}[/tex]

[tex]P=pgd=\delta d[/tex]

[tex]F=mg=pgAd[/tex]

---------------------------

The area of the ith strip is [tex]A_i=6\Delta y[/tex] so the pressure exerted on the ith strip is [tex]\delta d_i=pgd_i=pg(6-y_i^*)[/tex]

The hydrostatic force on the ith strip is [tex]F_i=\delta_iA_i=6pg(6-y_i)\Deltay[/tex]

The approximate force along the entire surface is therefore:

[tex]F_{net}=\lim_{n-\infty}\Sigma_{i=1}^n6pg(6-y_i)\Delta y[/tex]

[tex]=6pg\int_0^4(6-y)dy[/tex]

Am I setting this up correctly?