# Force exerted on a levee **URL:** \ **Category:** Factual Questions\ **Created:** [January 3, 2006, 2:37am UTC](https://boards.straightdope.com/t/force-exerted-on-a-levee/338173 "2006-01-03T02:37:35Z")\ **Posts on this page:** 12\ **Page:** 1
**Author:** ![carnivorousplant](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/carnivorousplant/32/3563_2.png) [@carnivorousplant](https://boards.straightdope.com/u/carnivorousplant)\ **Post date:** [January 3, 2006, 2:37am UTC](https://boards.straightdope.com/t/force-exerted-on-a-levee/338173/1 "2006-01-03T02:37:35Z")
How do you calculate it for say an 18’ high levee in New Orleans? ---
**Author:** ![Frank](https://avatars.discourse-cdn.com/v4/letter/f/3d9bf3/32.png) [@Frank](https://boards.straightdope.com/u/Frank)\ **Post date:** [January 3, 2006, 3:01am UTC](https://boards.straightdope.com/t/force-exerted-on-a-levee/338173/2 "2006-01-03T03:01:50Z")
This question probably has a factual answer. Moved from IMHO to GQ. ---
**Author:** ![treis](https://avatars.discourse-cdn.com/v4/letter/t/bc79bd/32.png) [@treis](https://boards.straightdope.com/u/treis)\ **Post date:** [January 3, 2006, 3:13am UTC](https://boards.straightdope.com/t/force-exerted-on-a-levee/338173/3 "2006-01-03T03:13:19Z")
Resultant force=1/2_p_g_D^2_W where p=density of water (1.94 lbm/ft^3), g=gravity (32.2 ft/s^2), D=depth of wather and W=width of submerged surface. ---
**Author:** ![Frank](https://avatars.discourse-cdn.com/v4/letter/f/3d9bf3/32.png) [@Frank](https://boards.straightdope.com/u/Frank)\ **Post date:** [January 3, 2006, 3:14am UTC](https://boards.straightdope.com/t/force-exerted-on-a-levee/338173/4 "2006-01-03T03:14:15Z")
> [@treis](#): > > Resultant force=1/2_p_g_D^2_W where p=density of water (1.94 lbm/ft^3), g=gravity (32.2 ft/s^2), D=depth of wather and W=width of submerged surface. This question definitely has a factual answer. ---
**Author:** ![carnivorousplant](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/carnivorousplant/32/3563_2.png) [@carnivorousplant](https://boards.straightdope.com/u/carnivorousplant)\ **Post date:** [January 3, 2006, 3:18am UTC](https://boards.straightdope.com/t/force-exerted-on-a-levee/338173/5 "2006-01-03T03:18:43Z")
Thank you. ---
**Author:** ![treis](https://avatars.discourse-cdn.com/v4/letter/t/bc79bd/32.png) [@treis](https://boards.straightdope.com/u/treis)\ **Post date:** [January 3, 2006, 3:31am UTC](https://boards.straightdope.com/t/force-exerted-on-a-levee/338173/6 "2006-01-03T03:31:54Z")
> [@carnivorousplant](#): > > Thank you. You’re welcome, I neglected to mention that W is the projected width onto the vertical plane. ---
**Author:** ![carnivorousplant](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/carnivorousplant/32/3563_2.png) [@carnivorousplant](https://boards.straightdope.com/u/carnivorousplant)\ **Post date:** [January 3, 2006, 3:52am UTC](https://boards.straightdope.com/t/force-exerted-on-a-levee/338173/7 "2006-01-03T03:52:01Z")
Do you have a link to how the equation was derived? Thanks again. ---
**Author:** ![AskNott](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/asknott/32/5790_2.png) [@AskNott](https://boards.straightdope.com/u/AskNott)\ **Post date:** [January 3, 2006, 4:33am UTC](https://boards.straightdope.com/t/force-exerted-on-a-levee/338173/8 "2006-01-03T04:33:11Z")
Isn’t it affected by the number of blues singers on the levee at the time of the breach? ---
**Author:** ![treis](https://avatars.discourse-cdn.com/v4/letter/t/bc79bd/32.png) [@treis](https://boards.straightdope.com/u/treis)\ **Post date:** [January 3, 2006, 4:42am UTC](https://boards.straightdope.com/t/force-exerted-on-a-levee/338173/9 "2006-01-03T04:42:42Z")
Can’t find a link but: dP/dD=p_g or in words the change in pressure over the change in depth is density tiems gravity. Multiplying by dy and integrating yields P=p_g_D+Constant. In this case the constant is zero becuase air pressure acts on all surfaces so P=p_g_D. In order to calculate the total pressure on the surface we write an equation for an infintesimally small piece of area and integrate. If you are facing the surface lets call X the horizontal axis and D is the verticle. Now, force is Pressure times area with our area being dX_dD. So our equation is F=P_dA=p_g_D_dX\*dD. We need to integrate that equation twice, for X from 0 to W where W is the width and for D from 0 to Y where Y is the depth. Now, since the pressure doesn’t vary in the X direction the integration results in W. That leaves us with F=W_p_g_D_dD. Since w, p and g are constants in the D direction we can pull them out of the integral. F=(W_p_g)_int(D,dD,0,Y). The integral of D is 1/2_D^2. We plug in our limits and find int(D,dD,0,Y)=1/2_Y^2. Putting that back in our equation we get F=W_p_g_Y^2/2. I don’t know if that explanation helps, I suspect it won’t, but I couldn’t find a good webpage. ---
**Author:** ![NinetyWt](https://avatars.discourse-cdn.com/v4/letter/n/cc9497/32.png) [@NinetyWt](https://boards.straightdope.com/u/NinetyWt)\ **Post date:** [January 3, 2006, 7:47am UTC](https://boards.straightdope.com/t/force-exerted-on-a-levee/338173/10 "2006-01-03T07:47:26Z")
[this](http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/Pressure/HydroStatic.html) was the best I could find after a brief look. ---
**Author:** ![carnivorousplant](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/carnivorousplant/32/3563_2.png) [@carnivorousplant](https://boards.straightdope.com/u/carnivorousplant)\ **Post date:** [January 3, 2006, 3:47pm UTC](https://boards.straightdope.com/t/force-exerted-on-a-levee/338173/11 "2006-01-03T15:47:56Z")
> [@treis](#): > > I don’t know if that explanation helps, I suspect it won’t, but I couldn’t find a good webpage. Well, I knew 1/2D^2 was in integral to find force over depth. 🙂 Thanks again. ---
**Author:** ![David\_Simmons](https://avatars.discourse-cdn.com/v4/letter/d/9de053/32.png) [@David\_Simmons](https://boards.straightdope.com/u/David_Simmons)\ **Post date:** [January 3, 2006, 5:47pm UTC](https://boards.straightdope.com/t/force-exerted-on-a-levee/338173/12 "2006-01-03T17:47:21Z")
> [@carnivorousplant](#): > > Do you have a link to how the equation was derived? > Thanks again. It’s just the volume of a right triangular prism 1 unit wide multiplied by the weight of the water in the prism and the length of the levee in the same units as those of the prism.