L-shaped Tank The L-shaped tank shown in Fig. 15-38 is filled with water and is open at the top.

step 1 All right. So for this example, we're given this figure in our book. And I do recommend going in

L-shaped Tank The L-shaped tank shown in Fig. 15-38 is...

Key Concepts

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid at rest due to the force of gravity. It increases linearly with depth, meaning that the pressure at any point in the fluid is directly proportional to the vertical distance below the free surface. This principle is fundamental in determining the distribution of pressure on the surfaces of submerged objects in fluids.

Force on Submerged Surfaces

The total force exerted on a submerged surface is calculated by integrating the pressure over the area of that surface. Since pressure changes with depth, different parts of the surface experience different amounts of force. Summing (integrating) these differential forces over the entire area gives the net hydrostatic force acting on the surface.

Integration of Pressure Distribution

To obtain the total force on a submerged plane surface, it is necessary to perform an integration over the area, taking into account both the variation of pressure with depth and the orientation of the surface. This approach is applicable whether the surface is vertical, inclined, or of a more complex shape, and it is essential for accurately analyzing the effects of fluid pressure on the structure.

Center of Pressure

The center of pressure is the point on a submerged surface at which the total hydrostatic force is considered to act. It is determined by the distribution of pressure over the surface and typically lies below the centroid of the area for vertically oriented surfaces. Understanding the center of pressure is key for designing structures to ensure that they can effectively resist the applied loads.

Transcript

0:00 All right.

00:02 So for this example, we're given this figure in our book.

00:03 And i do recommend going into the book and seeing what the actual figure looks like.

00:07 Mine is a little off, but it should, you know, serve its purpose for what we need it for.

00:13 So in part a of this question, we're told that we have this l -shaped tank and the top is uncovered, right? and it's filled with water.

00:26 So we know that the density of water is 1 ,000 kilograms per cubic meter.

00:31 We also know that the acceleration due to gravity is 9 .8 meters per second squared.

00:36 And they tell us that the value d is 5 meters.

00:42 So we're given this l shape tank.

00:44 And for part a, they want to know what the force acting on face a of our tank is.

00:53 Right so this is face a and they want to know what the force on face a is so two equations we're going to need to know are going to be our force equation which states that the force is equal to the pressure times the area as well as the pressure equation which states pressure is equal to the density of our liquid times the acceleration due to gravity times our height or our depth.

01:26 All right.

01:27 So we can actually combine these two equations and we'll get that the force is equal to the density times the acceleration of gravity, times the depth, times the area of what we're trying to measure the force on, right? so we know that our density is going to be 1 ,000 kilograms per cubic meter.

01:59 Acceleration to gravity will be 9 .8 meters per second squared.

02:05 The depth here we can see that it will be 3d minus 1d, right? so that tells us that our depth is 2d...

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