Written Report
Pascal's law or the principle of transmission of fluid-pressure is a principle in fluid mechanics that states that pressure exerted anywhere in a confined incompressible fluid is transmitted equally in all directions throughout the fluid such that the pressure variations (initial differences) remain the same. The law was established by French mathematician, Blaise Pascal.

This principle is stated mathematically as: * P=pg( h) * P is the hydrostatic pressure (given in pascals in the SI system), or the difference in pressure at two points within a fluid column, due to the weight of the fluid;ρ is the fluid density (in kilograms per cubic meter in the SI system);g is acceleration due to gravity (normally using the sea level acceleration due to Earth's gravity, in SI in metres per second squared); * h is the height of fluid above the point of measurement, or the difference in elevation between the two points within the fluid column * Pascal's law states that when there is an increase in pressure at any point in a confined fluid, there is an equal increase at every other point in the container. * A container, as shown below, contains a fluid. There is an increase in pressure as the length of the column of liquid increases, due to the increased mass of the fluid above. * For example, in the figure below, P3 would be the highest value of the three pressure readings, because it has the highest level of fluid above it.

* If the above container had an increase in overall pressure, that same added pressure would affect each of the gauges (and the liquid throughout) the same. For example P1, P2, P3 were originally 1, 3, 5 units of pressure, and 5 units of pressure were added to the system, the new readings would be 6, 8, and 10.

* Applied to a more complex system below, such as a hydraulic car lift, Pascal's law allows forces to be multiplied. The cylinder on the left shows a cross-section area of 1 square inch, while the cylinder on the right shows a cross-section area of 10 square inches. The cylinder on the left has a weight (force) on 1 pound acting downward on the piston, which lowers the fluid 10 inches. As a result of this force, the piston on the right lifts a 10 pound weight a distance of 1 inch.

* The 1 pound load on the 1 square inch area causes an increase in pressure on the fluid in the system. This pressure is distributed equally throughout and acts on every square inch of the 10 square inch area of the large piston. As a result, the larger piston lifts up a 10 pound weight. The larger the cross-section area of the second piston, the larger the mechanical advantage, and the more weight it lifts.

Pressure is the quantity which causes (or results from) fluid flow or sustains the weight of a column of fluid. Fluid pressure is defined as the normal force exerted on a surface (real or imaginary) in a fluid per unit area. When dealing with fluids contained in pipes or ducts, we shall assume pressure uniform over the cross section areas of the pipes or ducts. Therefore, the total axial force exerted on the cross section area is

where is the average bulk pressure over .
Pressure is measured in the unit called a pascal, Pa = N/m. Two other commonly used pressure units are the bar, bar = kPa, and standard atmosphere, atm = kPa. The absolute pressure is measured relative to absolute vacuum. Most pressure-measuring devices, however, are calibrated to read zero in the atmosphere, and so they indicate the difference between the absolute zero pressure and the local atmospheric pressure. This difference is called the gauge pressure. Throughout this text, the pressure will denote gauge pressure unless it is otherwise specified.

* The formulas that relate to this are shown below:

* P1 = P2 (since the pressures are equal throughout).Since pressure equals force per unit area, then it follows that * F1/A1 = F2/A2It can be shown by substitution that the values shown above are correct, * 1 pound / 1 square inches = 10 pounds / 10 square inchesBecause the volume of fluid pushed down on the left side equals the volume of fluid that is lifted up on the right side, the following formula is also true. * V1 = V2by substitution, * A1 D1 = A2 D2A = cross sectional area * D = the distance moved or * A1/A2= D2/D1This system can be thought of as a simple machine (lever), since force is multiplied. The mechanical advantage can be found by rearranging terms in the above equation to * Mechanical Advantage(IMA) = D1/D2 = A2/A1For the sample problem above, the IMA would be 10:1 (10 inches/ 1 inch or 10 square inches / 1 square inch).

ANIGAN, CHRISTIAN L. 2012-10996