Pascal's Law and pressure difference experiment for Science Fair Project

What is Pascal's Law?

     It is the basic principle for the transmission of fluid pressure through the same solution. This gives a new field of study fluid mechanics. This fluid mechanics law was established by French mathematician Blaise Pascal in the year 1647–48 with definition, hydraulic application, pressure difference experiment and formula. It is called Pascal's law. This Pascal's law can be used for a science fair project for 8th and  9th students.

Photo by Gerold Hinzen on Unsplash

Definition of Pascal's Law

      In definition pressure also derived from the force as similar to energy. The pressure is calculated from the force acting to any surface divided by area of the surface. If the pressure is applying along with the solution (water), the pressure has conversed in any dimension. The pressure is conserved in large and small dimensions.

              Pressure in small dimension = Pressure in large dimension

         (Force/Area) in small dimension  = (Force/Area) in large dimension

 In another way, Pascal's Law is defined as " A change in the pressure gradient of the hydraulic solution at any point in a confined hydraulic fluid solution at rest is transmitted to all points in the hydraulic fluid solution"

Alternate definition:"The pressure gradient of the hydraulic solution applied to any part of the confined hydraulic liquid will be transmitted uniformly in all the direction through the hydraulic solution in conserve form"

This Pascal law's principle is stated as the following formula:

                                ⧍P =𝛒g(⧍h)

    Here, ⧍P is the hydrostatic pressure which measures in pascals with SI unit system. The pressure difference at two points within the enclosed space of the fluid column. It is mainly due to the weight of the fluid liquid. 𝛒 is fluid density which measures in kilogram per cubic meter in SI unit system. g is gravity due to acceleration( meter per second square). ⧍h is the difference in height with the application of pressure which measures in meter with SI unit system.
 
      Fluid density is not static. If the fluid is viscous, it won't change. In viscous fluid, pressure transmission is very difficult. If the fluid is dilute one, then it will transmit very easily. In dilute fluid liquid, pressure transmission is easy. the hydraulic solution should be in moderate viscosity.

Explanation and application of Pascal's law:   

    In fluid mechanics, pressure can lower into higher in the same enclosed liquid with a different dimension of liquid occupied or the weight of the solution in different parts. We can explain this hypothesis with following diagram.

Pascal's Law: Diagrammatic representation

    In the diagram, the part A is narrow in dimension as compare with part B. Both parts A and B are closed with piston pis1 and pis2 respectively. The piston is circular in shape. If pressure P1 is applying through piston pis1in part A, then it develops pressure P2 through pis2 in part B. Force F1 and F2 are from P1 and P2 respectively.

     Here, Force F2 is much greater than from Force F1. How is it possible to convert small to higher force? in the hydraulic pump as in the diagram, the weight of the fluid liquid in part A is smaller than part B. From classical physics, the mass of fluid liquid is directly proportional to the pressure of the liquid. If the mass of the fluid is high, then pressure is high on it. similarly, if the mass of the fluid is low, then the pressure is also on it.

    In addition, the explanation from quantum molecular physics, part A the fluid liquid molecule has come closer to one another in the smaller space. Thus, it develops more pressure in that particular region. For example, the water molecule is used as fluid liquid. In liquid form, it undergoes hydrogen bonding with its neighbor molecules. It creates a very good amount of hollow space inside the liquid water.

   In a smaller space of part A, water molecules come closer to one another under small pressure application. When the molecule comes closer to one another after the limiting distance, it starts to repel each other. So the force or pressure builds at that region, which transmits the from part A to part B of the same enclosed water liquid of the region.

Science Project Idea with Pascal's law

  This experiment and information are useful for science fair project for 8th and  9th students. The following materials are required for the pressure difference experiment with the application of Pascal's law.

Material required for prPascal's Law and pressure difference experiment for Science Fair Projectessure difference experiment:

1. U tube                      -------                 One
2. Beaker                     --------                One (5 liters)
3. Funnel                      --------                One
4. Plastic tube              --------                One
5. Scale measuring      --------                One pair(50 cm)
6. Salt  (NaCl)               --------                One (500 gm)
7. Sugar                        --------                One (500 gm)
8. Edible red dye          --------                One
9. Purified water          --------                15 liters 

Illustration: Pascal's law experimentation

Standard Operating Protocol for pressure difference experiment:

1. Take U tube and fill with purified water make it equally in two sides and 3 drops of edible dye into it.
2. Take the Beaker and fill with 3 liters of purified water.
3. U tube is connected with funnel through the plastic tube.
4. One measuring scale is connected with a beaker another is connected with U tube.
5. Move the funnel near to the beaker water surface and slowly move downwards to the bottom of the beaker. (as given in figure)
6. Note down the height of the beaker with the funnel in the record notebook.
7. Similarly, U tube height difference is to note down in the record notebook.
8. The same experiment can be repeated for different concentrations of salt (NaCl). ( at least do 5gm, 10gm, 20gm, 50gm, and 100 gm)
9. In another way, These experiments can be repeated for different concentrations of sugar. (at least do 5gm, 10gm, 20gm, 50gm, and 100 gm)

Observation from this pressure difference experiment:

        We can measure the pressure difference from the 3 L water beaker in different height levels. At the same time, we can measure the height difference from the U tube. We can tabulate the reading U tube height difference and funnel height in the beaker. From the above Pascal's law equation, we can calculate the pressure difference in the beaker.

      If plot pressure difference vs height difference in the beaker, the slop of this plot gives the density of the water. similarly, we can repeat the same experiment for salt and sugar solution. Finally, we can calculate the density of the salt solution and sugar solution of different concentrations.

Note: U tube is used to measure the pressure difference with the height difference in the U tube. Beaker height should be marked with a marker. From this pascal's law experiment result can present in the science fair project for 8th and  9th students.


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${\displaystyle \Delta P=\rho g(\Delta h)\,}$

${\displaystyle \Delta P}$