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Things you should know
The pressure is defined as thrust (which is a force acting perpendicular to a surface area) per unit area. In other words, it is a calculation of how much perpendicular force is acting on a unit surface area of the object.
It can be calculated using the following formula:
Pressure(P)=(Thrust (F))/(Area (A))
Or;
P=F/A
The pressure is measured in Pascals or it is just written as Pa.
Activity
1. Find out the equivalent unit for Pascal or Pa.
PASCAL's LAW
Pascal’s law states that the pressure exerted to a confined liquid is transmitted equally and undiminished in all directions throughout the mass of the liquid.
Consider following syringe (such syringe is called Pascal’s syringe because he invented it) to understand what Pascal’s law means. The design of the syringe is such that it consists of a piston connected to a sphere with holes and is filled with fluid as shown in the figure below.
When the piston plunger is depressed (meaning the pressure is exerted), the confined fluid in the sphere shoots out of the holes with equal force (meaning the pressure is transmitted equally) in all directions. This is a simple proof of Pascal’s law.
Activity
If possible, create your own, kind of, Pascal’s syringe using a plastic bottle (preferably a disposable plastic water bottle) to confirm Pascal’s law by yourself. Follow the following steps.
Step 1: Fill the water bottle up to its rim with water and close the bottle tightly.
Step 2: Now, using a needle carefully puncture the water bottle to make a hole. Make sure the holes are of the same size. Also, make sure there is a good number of holes. Precaution: Please, be careful while using a needle to make holes.
Step 3: Slowly open the bottle cap and notice the water coming out of the holes.
1. Explore: Why do you think the water comes out of the holes only when the bottle caps are open and not when it is closed?
2. Does the water coming out of the holes cover equal distances? What could this mean?
Application of Pascal’s Law
Some of the applications of Pascal’s law is in hydraulic machines commonly used in excavators, car brakes, etc. In other words, they work base on the principle of Pascal’s law.
These machines act as force multipliers. That is, the output force is always greater than the input force.
Construction and Working of Hydraulic Machines
The diagram below represents the basic construction and working of such machines. Let us find out how these kinds of machines function.
The blue colour in the above construction represents liquid. Notice that, the piston 1 is much smaller compared to piston 2 and that the force is applied to (input force) piston 1 to get the output on the piston 2. The areas of the pistons are coloured black.
Say the force applied to piston 1 is F_1 and its area to be A_1, then the pressure (P_1) exerted on the piston 1 is equal to F_1/A_1 .
That is;
P_1=F_1/A_1
Similarly, the pressure (P_2) exerted on the piston 2 is equal to F_2/A_2
That is;
P_2=F_2/A_2
As per Pascal’s law, the pressure inside the confined liquid is the same. This means;
P_1=P_2
In other words:
P_1=F_1/A_1 =P_2=F_2/A_2
Or;
F_1/A_1 =F_2/A_2
That is;
F_1=F_2/A_2 ×A_1 or F_2=F_1/A_1 ×A_2
Or;
F_1=P_2×A_1 or F_2=P_1×A_2
Since, P_1=P_2 according to Pascal’s law (as already stated above) and from the diagram we have, A_2>A_1 (A_2 greater than A_1), we can conclude that F_2 is greater than F_1 (F_2>F_1).
Activity:
1. What would happen to the output force if the area of the piston 2 is made larger?
Let explore the following example to understand better. Note that there are only four things that you have to remember from this exercise.
Pressure at P_1 is given by the following formula
P_1=F_1/A_1
That is;
P_1=10N/〖2m〗^2
∴ P_1=〖5N/m〗^2
According to Pascal’s law, we know;
P_1=P_2
That is, the pressure at piston 2 (P_2) is also 〖5N/m〗^2 or 5 Pa.
Let us calculate the output force〖 (F〗_2) on piston 2. Say that the area (A_2) of piston 2 is 4m^2.
We know;
P_2=F_2/A_2
That is;
F_2=P_2×A_2
Or;
F_2=〖5N/m〗^2× 4m^2
∴F_2=20N
4. (Conclusion) If we compare the input force (10N) and the output force (20N), we see a huge difference. The output force is much greater than the input force. This is the reason why hydraulic machines are used as force multipliers.
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