If youve ever swam to the bottom of a pool, youve probably felt your ears make a popping sensation. This is due to a property of fluid known as pressure, and is responsible for a wide variety of physical phenomena (such as explosions and vacuums). Pressure is the build up of a force on an object - the stronger the pressure, the more force an object feels. The pressure exerted by a fluid is uniform throughout the system, which gives way to Pascals principle. Basically, this principle will be useful in determining the area or force exerted on one end of a fluid system if you know the other.
Pressure is the effect of a force acting upon a surface. It is a scalar, and is measured in N/m^2, or Pascals.
Atmospheric pressure (P_0) is 101,325 pascals.
Pressure exerted by a fluid on an object submerged in that fluid can be calculated by multiplying the density of the fluid by the acceleration due to gravity, and multiplying that by the depth to which the object is submerged (h). This is known as gauge pressure.
If there is also atmosphere above the fluid, the absolute, or total, pressure can be obtained by adding in the atmospheric pressure.
Pascal's Principle states that when a force is applied to a contained incompressible fluid, the pressure increases equally in all directions throughout the fluid.
Pascal's Principle drives the operation of hydraulic lifts, in which two pistons of different areas are combined with an incompressible fluid. F1/A1=F2/A2
Pressure & Pascal's Principle
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Hi everyone. I am Dan Fullerton and I would like to welcome you back to Educator.com. 0000
Today we are going to continue our study of fluids as we talk about pressure and Pascal's principle. 0004
Our objectives are going to be to calculate pressure as the force a system exerts over an area, to explain the difference between gauge pressure and absolute pressure, and explain the operation of a hydraulic system as a function of equal pressure spread throughout a fluid. 0009
Pressure -- pressure is the effect of a force acting upon a surface. 0025
It is a scalar. It is a force per unit area and its units are Newtons per meter squared (N-m2), which are also known as Pascal's, which we typically abbreviate as (Pa). 0030
If pressure if force per unit area, our formula for pressure is P = F/A. 0040
Now it is important to know that the force is always perpendicular to the surface it is acting on. 0047
Exerting pressure -- all states of matter can exert pressure. 0063
You walk across an ice covered lake, you exert pressure on the ice equal to your weight, divided by the area, which contacts the ice. 0067
That is why if you do not want to crack the ice, they teach you to spread your hands and feet out to spread out that force over a larger area, so you get less pressure. 0074
If you walk on snow with snow shoes with large areas of contact, you increase the area; you reduce the pressure and you walk on top of the snow, that is why they are so big -- larger area. 0085
Now, fluids exert outward pressure in all directions on the sides of any container holding the fluid. 0096
Rank the following from highest pressure to lowest pressure upon the ground. 0301
The atmosphere at sea level -- well that we know is right around 100 Pa. 0305
A 7,000 kg elephant with total area of 0.5 m2 in contact with the ground -- well pressure will be force/area or that will be 7,000 kg × g (10)/area of 0.5 or about 140,000 Pa. 0313
A 65 kg lady in high heels with a total area of 0.005 m2 in contact with the ground -- if pressure is force/area, that will be 65 kg × 10 m/s2/area (0.005) or about 130,000 Pa. 0336
And finally a 1600 kg car with a total tire contact area of 0.2 m2 -- the pressure equals force over area, so that will be 1600 kg × 10 m/s2/0.2 m2 or about 80,000 Pa. 0363
So, if I were to rank these from highest pressure to lowest pressure, I would start with the elephant (B), go to the lady in high heels, atmospheric pressure, and finally the car, so (B), (C), (A), (D). 0384
Let us talk about pressure on a submerged object. 0404
The pressure a fluid exerts on an object submerged in that fluid is determined by multiplying the density of the fluid by the depth submerged, all multiplied by the acceleration due to gravity. 0407
We call that the gauge pressure, which is ρ (density) × (g) × (h). 0417
If there is also atmosphere above the fluid, such as the situation here on Earth, you can determine the absolute or total pressure by adding in the atmospheric pressure which we will write as P0, which is about 100,000 Pa. 0423
So absolute pressure is atmospheric pressure plus gauge pressure -- P0 + ρ, where ρ is the density of the fluid, (gh). 0435
When a force is applied to a contained incompressible fluid, the pressure increases equally in all directions throughout that fluid. 0533
This is the foundation for hydraulic systems and things like barber shop chairs, construction equipment, and even car brakes. 0540
In car brakes, in the movies, you will even sometimes see people cut the brake lines so the brakes do not work -- the fluid leaks out and the brakes no longer work because the fluid is no longer contained. 0548
It must be a contained fluid or incompressible or nearly incompressible fluid. 0558
Let us talk about force multiplication using Pascal's principle, also known as the basis of hydraulics. 0566
To begin with, we have a force (F1) that we are applying to a piston of area (A1) and that is going to create a pressure of (P1), so (P1) is caused by force (F1) applied to a piston of area (A1) on a contained, incompressible fluid -- we have a closed container, incompressible fluid here. 0573
Now over on the right hand side, the pressure on this piston, must be F2/A2. 0594
Why? By Pascal's principle, you must have the same pressure anywhere throughout the fluid. 0601
Well when you do that, let us take a look at the ramifications. 0607
If P1 = P2, by Pascal's principle, then that means F1/A1 = F2/A2 or if I cross-multiply (F1)(A2) = (F2)(A1) or F2 = A2/A1 × F1. 0611
What does this mean? You have increased the force -- if you apply a force (F1) and you have a different area on your two pistons, you can increase that force by the ratio of the areas. 0637
If (A2) is five times larger than (A1), and you apply force (F1), you get five times that force on (F2).0650
You have effectively increased your applied force. 0658
Now you do not really get anything for free here. 0661
What you are going to end up having by conservation of energy is you are also going to have to push this piston five times further or you will get 1/5 the displacement that you would over here for the same displacement over there. 0665
The total work done on each side has to be the same for conservation of energy, and that is going to be by the same ratio as the area multiplier, but you can multiply a force if the areas are a ratio of 100:1, you have increased your force by a factor of 100 and that is the principle behind hydraulic systems. 0678
Let us take the example of a barber's chair when we apply this. 0699
A barber raises his customer's chair by applying a force of 150N to a hydraulic piston of area 0.01 m2. 0702
If the chair is attached to a piston of area 0.1 m2, how massive a customer can the chair raise?0711
Well, to solve this problem let us first determine the force applied to the larger piston. 0721
We know (F2) must be equal to the ratio of the area, A2/A1 × F1, therefore, F2 = 0.1(A2)/0.01(A1) = 10 × F1 (150N) = 1500N. 0728
This is the largest applied force you can have. 0750
Now then, if we want to know how massive a customer the chair can raise, if our force is 1500N, that must be equal to the weight -- the maximum that we can handle -- therefore, the mass that you can handle is 1500N/g (10 m/s2) or 150 kg. 0758
Now that 150 kg -- five of those kg have to be the chair, therefore, you could lift a customer of 145 kg, which is about 300 lbs. 0782
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