El tubo de entrada que suministra presión de aire para operar un gato hidráulico tiene 2 cm de diámetro. El pistón de salida es de 32 cm de diámetro. ¿Qué presión de aire se tendrá de aire se tendrá que usar para levantar un automóvil de 17,640 N?`

P₁ = 219.3 Pa

Explanation:

This fluid mechanics problem, we can use that the pressure is distributed with the same value throughout the system, which is Pascal's principle.

Let's use the subinidce1 for the small diameter and the subscript 2 for the larger diameter.

              P₁ = P₂

pressure is defined by

             P = F / A

we subtitute

             F₁ / A₁ = F₂ / A₂

             F₁ = F₂ A₁ / A₂

the area in a circle is

             A = π r² = π d² / 4

we substitute

            F₁ = F₂ (d₁ / d₂)²

we calculate

           F₁ = 17640 (2/32)²

           F₁ = 68.9 N

Having the force to be applied we can find the air pressure on the small plunger

          P₁ = F₁ / A₁

          P₁ = F₁ 4 / π d₁²

let's calculate

          P₁ = 68.9 4 / (π 0.02²)

          P₁ = 219.3 Pa

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