 So we're continuing on with looking at computing the forces on a submerged curved surface and in the last segment what we did is we found the forces that are acting on the curved surface we're making an approximation so we're finding resultant forces now what we want to do is we want to find out where those forces are acting if you're called for planar surfaces that was the center of pressure so essentially we're looking for the center of pressure for this curved surface and what I'm going to do I'm going to redraw our fluid chunk which is above the curved surface and we're going to rearrange and define some things that will enable us to then determine the location of where these forces are acting okay so here we have a schematic of our surface that we're interested in remember this is the surface here in the last segment we came up with an expression for f r y and f r x however we were not able to or we have not yet done is determine where these forces are acting and so those are the unknowns that we have the way that we're going to do this it'll be very similar to what we did for the planar flat plate and if you recall there we some moments about some location and for here what we're going to be doing is something moments about the origin that we'll call oh I've introduced a coordinate system with respect to that origin and that is the x and the y that we have on this plot so what we're going to do we're going to look at all the forces that we have acting we have f l we have f t we have weight and then we have f r y and f r x those are the forces will some moments and then try to figure out where the location is for those two forces the f r x and f r y okay so that's the equation that we get for the summing of the moments now there are a couple of things we can say about this expression first of all all of these terms here are known and the other thing that we know we from the last segment determined the forces so those are known as well so the unknowns we have two unknowns this and this and we only have one equation and what we're going to do we're going to make a bit of a general rule assumption for the vertical surface and the f l and the f r x force so let's take a look at that now okay so we have this as being a general rule so what is that saying well if we look at our curved surface recall we had this force here but we also have a projection of that area on this surface here and so that was the force in the x direction f r x and we also had a force this way which was f l but it turns out those two are essentially the same equal and opposite and they're acting at the same location so this here we said was y l y one was here it turns out y one is equal to y l and they're equal and opposite to one another so that's something that we will use to be able to simplify the equation we have for summing of the moments so let's take a look at that so we get f l is equal to f r x and y one is equal to y l and if you recall y l is the center of pressure of the vertical surface ac so with that we can look back to our analysis for planar surfaces and that tells us that f r x x at it will be the center of area of the surface ac and we need to find the center of pressure here so we have this term and so we get that expression now what we can do we can go in and determine i x x theta and a ac a ac if you recall is this surface here we have a to c so what we're talking about is this surface right here so let's look at the values we have theta theta for that is equal to 90 degrees i x x b l cubed divided by 12 using the dimensions that we have from our schematic we have l being that dimension we said it's width b into the screen and finally the area of ac is just b the depth or width into the screen times l which was the height so we have those we can plug them into the equation and with that we get y one we get y one is that it's just the center of area of ac modified and if you recall earlier so if this is the center of area here the center of pressure is going to be a little bit below and that determines y one now what we will do we'll go back to our moment equation summing of the moments so this equation here and we're going to plug in what we now know in order to try to isolate in this case we're going to be trying to isolate x one so let's work that through so we get the equation for x one and we plug in the values and finally we can solve for x one as being the following so that gives us the equation for the x component of the resultant force on our fluid element so what we had we had a plane or a curved surface under the water we said that that was a we put that as being b and we put that as being c let me double check to make sure that was right uh no i goofed that up i apologize about that so we had those flipped around that was a that is b and that is c double check to make sure b was on the right yeah okay so we have that and what we did is we solved for these forces here which we had f r x and f r y but what we were doing now is trying to figure out where they act and what we did is we defined y one as being this direction and then x one is being uh in this direction both from this origin so the force acting it could be something like that and then it would be like that on the surface and and that would then give us so the center of pressure is not exactly right on the surface as we get from this analysis but it's an equivalent force and consequently it gives us an indication as to where the center of pressure would act if you went through and you did the full complete complex integration that we looked at at the beginning of this segment so that is forces on a curved surface obviously a planar surface is a little easier but curved surfaces are a little bit more complex and this is a technique to enable you to figure out what that force would be and where it would act