Question

Calc: Find the force against the vertical end of a tank containing water weighing 62.4 lb/ft^3 as an integral with respect to y
The tank end is shaped like the bottom half of a semicircle, with radius 3ft

Answer 1

You can start with:
\[F = \int P\space dA\]

Answer 2

The area of the base is \(A = \pi R^2/2\), so \(dA = \pi R\space dR\)

Answer 3

the pressure is \(P = \rho gy\)

Answer 4

Whoa whoa whoa

Answer 5

Thats not the equation we were given

Answer 6

We were given F=int(whA)

Answer 7

And that pressure equation is different too

Answer 8

We were given p=wh

Answer 9

@jim_thompson5910

Answer 10

@thomaster @aaronq @e.mccormick

Answer 11

check out this page

http://www.math.ucsb.edu/ugrad/fluid.pdf

Answer 12

I mean I get parts of it, but I always have the length wrong

Answer 13

need help?

Answer 14

Yes please!!!

Answer 15

I always think that I have it correct, but I'm usually wrong

Answer 16

there are two pressure equations, depending on whether you are given the 'mass' density or the weight density.
in this problem you are given the weight density, pound / ft^3
so you dont need to multiply by g

Answer 17

ok

Answer 18

for weight density:
$$ P = \rho h$$
for mass density
$$P = \rho gh$$

Answer 19

We weren't even given the second one. The only equations we got were fluid pressure (p)=weight density x height and fluid force=p(weight density)(area)

Answer 20

And I always get hung up on the area

Answer 21

Actually I messed up the second equation. Its fluid force=whA

Answer 22

Pressure = Force / Area
so
Force = Area * pressure = A * wh

Answer 23

We weren't given the first equation either

Answer 24

I'm confused about how to get A in the formula

Answer 25

Like for this problem, I did \[\sqrt{9-y^2}dy\] as my area, but apparently its wrong

Answer 26

one moment

Answer 27

ok thanks

Answer 28

$$

\Large \Delta F_i = \rho (c - y_i) w(y_i) \Delta y $$

Answer 29

You're going to have to explain that formula to me

Answer 30

I moved the axis up 3

Answer 31

imagine that the trough end is like a vertical plate that you are submerging in water, (but the vertical plate has the shape of a semicircle

Answer 32

Down 3

Answer 33

Sorry!!

Answer 34

perl, it says "The tank end is shaped like the bottom half of a semicircle"

so the rectangular strips should be on the other side of the circle