# Hydrostatics

by Jared Rovny
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00:01 Now that we finished the mechanics aspect of this course covering the equations of motion, force, as well as energy and momentum, we’re ready to move on to some more applied situations.

00:13 We’re going to start with fluids and get started with that first. The first thing I need to let you know is where we’ve been and then how that contextualizes with where we’re going. We started with the equations of motion. We then moved on to discuss Newton’s laws, especially Newton’s second law. We discussed rotating objects using the force which is giving us torques.

00:35 We then finished our mechanics section with the discussion of the conserved quantity of energy as well as work which is changes in energy, as well as the conserved quantity of momentum.

00:45 These were all of our mechanics which we've summarized right up at the top here: the equations of motion, Newton’s laws and force, as well as energy, work, and momentum. We’re now ready to get into some more applied and practical situations including fluids and gases; electricity; circuits and magnetism; waves, sound and light; atoms and the atomic structure when we zoom in; and then thermodynamics and thermochemistry to finish. We’re going to start with fluids.

01:11 That’s what we’re going to do right now. We’ll start with just hydrostatics. Then we’ll move to idealized hydrodynamics where we allow fluids to be moving through a system including blood through your veins or arteries. We’ll finish up with some applied hydrodynamics, talking about more real world situations including a little bit more complexity. We’re going to start with a simple hydrostatics in which we’re not talking about flowing water just yet. In hydrostatics, we can discuss the properties of fluids, hydrostatic pressure, Archimedes’ principle, and Pascal’s law. We’ll do these each in turn starting with the properties of fluids. A few fluid properties that are important to know as well as for any material would be for example the density which simply measures how much mass we have per unit volume of material that we have. So, the density is signified by the symbol ρ. This is a Greek letter, rho. It is equal, the density, to the mass divided by the volume of a given object. Here are some example densities that you can look at just for reference. We have wood and water and steel. You can see that wood is less dense than water.

02:23 You can see that steel is far more dense than water which is of course why wood would float and where steel would sink. We could also define specific gravity. This is simply a way of measuring density relative to water. So, if our density is more than water or less than water, we can tell this very quickly. So, we define the specific gravity of any substance as the density, ρ of that substance divided by the density of water. So, using these same three quantities, wood has a density of half of water’s density. So, it has a specific gravity of 0.5. Water, by definition, has a specific gravity of 1 since it has its own density. Then steel has a specific gravity of 8 being eight times more dense than water. One thing very important to notice is that we’re going to talk about fluids but gases, just like air are also fluids. They have very different properties, certainly different densities.

03:16 But they flow and will behave using many of the same laws that water, which as a fluid will follow as well.

03:23 One key difference is that whereas a gas, if I for example, put it into a piston and tried to compress it, will compress. Both the volume and the pressure of the gas will change if I try to compress it, whereas for fluids, we’ll consider a simple, idealistic case of incompressible fluids. Namely, if I tried to apply some sort of pressure to my fluid and press it down in a piston like you see here, the volume will not be able to change. It’s stuck because it’s incompressible. The pressure can change in a fluid. Let’s start with another example of a property of fluids which is the surface tension.

04:00 A good analogy for surface tension will be something like a rope like you see here. If I’m pulling on both sides of the rope, what’s going to happen is the rope will try to fight that pulling.

04:08 It has chemical bonds trying to keep it back together even though I apply a mechanical force.

04:13 If we look at a liquid, we’ll have the same kind of thing happening. With a liquid, we’ll be pulling up against the walls of its container via an adhesion force which is a force of objects with things that are dissimilar from themselves. This will be fought with a cohesion force which is these water molecules or fluid molecules pulling towards each other and having a force of the molecules one to the other. If these forces are always pulling at every point in this fluid or every point in this example of a rope, then this pulling factor from the rope, for example, let’s just take a look at that rope and imagine that we’re actually pulling out on the sides very hard. If I introduced some cut into the rope for example so that the rope wasn’t able to maintain that molecular pull, that point, the point where I cut the rope is going to start to open and expand because of all the forces pulling it outwards. Similarly with a liquid, if I drop something into the liquid like a soap, that would ruin that cohesive force between the water molecules.

05:12 The forces outside at that point where I’ve ruined the surface tension would still be pulling.

05:17 All those adhesive and cohesive forces are still applied. We will see the water on the surface pull away from itself which is actually something you can visualize in your own experiments.

The lecture Hydrostatics by Jared Rovny is from the course Fluids.

### Included Quiz Questions

1. 5000 kg/m3
2. 500 kg/m3
3. 5 kg/m3
4. 0.05 kg/m3
5. 0.005 kg/m3
1. 3.5
2. 35
3. 3.5 g/cm3
4. 35 g/cm3
5. Cannot be determined without the volume
1. The water molecules are all attracted to each other (cohesion) and to the walls of the container (adhesion), such that there is a tension at equilibrium.
2. The water molecules are all attracted to each other (adhesion) and to the walls of the container (cohesion), such that there is a tension at equilibrium.
3. The water molecules are all repelled from each other (cohesion) and from the walls of the container (adhesion), such that there is a tension at equilibrium.
4. The water molecules are all repelled from each other (adhesion) and from the walls of the container (cohesion), such that there is a tension at equilibrium.
5. The water molecules feel no effect on each other, but the attraction to the walls of the container causes a tension at equilibrium.
1. 3 g/cm3
2. 3 kg/m3
3. 3000 g/cm3
4. 3000 kg/cm3
5. This cannot be answered without knowing the volume

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