 We're now going to take a look at hydrostatic forces on submerged curved surfaces. So we've already looked at this on planar surfaces and for that we came up with a series of equations and the way that we did that is we went through an integration procedure and so we could do that integration again. However it would be a little complex. This is what would be involved. So this was the equation that we integrated when we're looking at planar surfaces and for planar surfaces the area was kind of easy. When we're dealing with curved surfaces we could have a much more complex surface and consequently it can be a little bit on the laborious side and as a result what we're going to do we're going to look at a bit of a shortcut and that's what we'll talk about in the next two segments. So to begin with what I'll do is I'll draw a schematic that we'll be referring to as we go through the derivation. Okay so this is the curved surface that we're dealing with and we're trying to determine the forces on the curved surface which is submerged below the surface of some liquid and what we're going to do we're going to simplify matters by creating this chunk of fluid that is above the plate and we'll say that on the upper surface of the chunk of fluid we have a force Ft. There is a force acting on the left-hand side of the fluid and that will be at the center of pressure of this surface AC. This is the center of area of AC. And we're going to go through and use this schematic as the starting point for our analysis and the way that we're going to begin the analysis is we're going to sum forces on the fluid mass ABC. So that will be the chunk of fluid that is essentially right in here inside of this area that is drawn out with the curved surface and when we sum forces we equal them to zero so what we will do will begin by summing forces in the y direction. So the y direction looking back at our schematic in the y direction what do we have? We have this force we have the weight and we have Fry and those all equal zero. For the force on the top that is going to be this depth H1 and that will give us the hydrostatic pressure multiplied by the area and the area there would be CB so this is assuming unit depth that we're looking at and that's why we've defined that as being ACB and with that we can write Fry. So this is the hydrostatic pressure at the top of that surface CB multiplied by the area plus the weight of the fluid element itself which is in the curved surface that gives us Fry so that is the force in the y direction. Now what we're going to do let's take a look at the force in the x direction and the force is involved here is going to be the hydrostatic force here at the center of pressure as well as the reaction force. Now the hydrostatic force is going to be the pressure at the center of area of AC there's our diagram so it's going to be of this area here AC where A and C is there. So with that we can write out the force the reaction force in the x direction and here H that's the center of area of a surface AC and one thing that we can note we have pressure atmosphere here if it turns out for our particular system that we're looking and we have p atmosphere out here we can neglect that atmospheric pressure from the equation that we have. Okay so there what we have is we have an expression for Fry and we have an expression for FRx for right now however we're not really sure where those are acting and in order to figure out where they're acting just like when we looked at planar surfaces what we had to do we had to go through some moments and so that's what we're going to do in the next segment we're going to some moments in order to figure out where those forces are acting on the curved surface.