If an
oscillating U-tube is filled with water and pistons are placed at each end, pressure exerted by the left piston will be transmitted throughout the liquid and against the bottom of the right piston. (The pistons are simply "plugs" that can slide freely but snugly inside the tube.) The pressure that the left piston exerts against the water will be exactly equal to the pressure the water exerts against the right piston p_1 = p_2. By using p = \frac FA we get \frac{F_1}{A_1} = \frac{F_2}{A_2} \Leftrightarrow \frac{F_2}{F_1} = \frac{A_2}{A_1}. Suppose the tube on the right side is made 50 times wider \frac{A_2}{A_1} = 50. If a 1 N load is placed on the left piston (F_1 = 1N), an additional pressure due to the weight of the load is transmitted throughout the liquid and up against the right piston. This additional pressure on the right piston will cause an upward force F_2 = F_1 \frac{A_2}{A_1} = 50N which is 50 times bigger than the force on the left piston. The difference between
force and
pressure is important: the additional pressure is exerted against the entire area of the larger piston. Since there is 50 times the area, 50 times as much force is exerted on the larger piston. Thus, the larger piston will support a 50 N loadfifty times the load on the smaller piston. Forces can be multiplied using such a device. One
newton input produces 50 newtons output. By further increasing the area of the larger piston (or reducing the area of the smaller piston), forces can be multiplied, in principle, by any amount. Pascal's principle underlies the operation of the
hydraulic press. The hydraulic press does not violate
energy conservation, because a decrease in distance moved compensates for the increase in force. When the small piston is moved downward 100 centimeters, the large piston will be raised only one-fiftieth of this, or 2 centimeters. The input force multiplied by the distance moved by the smaller piston is equal to the output force multiplied by the distance moved by the larger piston; this is one more example of a simple machine operating on the same principle as a
mechanical lever. A typical application of Pascal's principle for gases and liquids is the automobile lift seen in many service stations (the
hydraulic jack). Increased air pressure produced by an air compressor is transmitted through the air to the surface of oil in an underground reservoir. The oil, in turn, transmits the pressure to a piston, which lifts the automobile. The relatively low pressure that exerts the lifting force against the piston is about the same as the air pressure in automobile tires. Hydraulics is employed by modern devices ranging from very small to enormous. For example, there are hydraulic pistons in almost all construction machines where heavy loads are involved. Other applications: • Force amplification in the
braking system of most motor vehicles. • Used in
artesian wells,
water towers, and
dams. •
Scuba divers must understand this principle. Starting from normal
atmospheric pressure, about 100
kilopascal, the pressure increases by about 100 kPa for each increase of 10 m depth. • Usually Pascal's rule is applied to confined space (static flow), but due to the continuous flow process, Pascal's principle can be applied to the
lift oil mechanism (which can be represented as a U tube with pistons on either end). ==Pascal's barrel==