Physics Help please!!!! Its on density, force, load...etc...?

Question

Here are some problems that I am having problems with:

1) In a car lift used in a service station, compressed air exerts a force on a small piston of circular cross-section having a radius of 3.84 cm. This presure is transmitted by a liqud to a second piston of radius 24.1 cm. What force must the compressed air exert in order to lift a car weighing 11500 N? answer in N

2) What air pressure will produce this force? answer in units of Pa

3) Assume the density of sea water is 1024 kg/m^3 and take the atmostpheric pressure equal to 101000 Pa.
The acceleration of gravity is 9.8 m/s^2. Calculate the pressure at an ocean depth of 1240m. Answer in unts of Pa.

4) Calculate the total force exerted on teh outside of a circular sbmarine window of a diameter 43.7 cm at this depth. answer in uits of N.


Thank you for any help!

Answer 1

1) I'll assume you're acquainted with Pascal's Principle. Since fluid pressure can be regarded as the same in every part of the fluid,

p = f/A = f'/A', or
f = f' A/A' = f' (r/r')² = 11 500 (3.84/24.1)² = 292 N.

Radius ratio is squared because area (of pistons) is proportional to square of piston radius.

2) p = f/A = 292 N/(π r²) m² = 292 N / (π (3.84 E-2)²) m² = 63.03 E3 Pa = 63 kPa. Piston area must be in m², in order to obtain Pa.

3) Hidrostatic pressure:

p = ρgh = 1 024 kg/m³ × 9.8 m/s² × 1 240 m = 12.445 E6 kg m/m² s² = 12.44 MPa. This is "gauge" pressure. In order to get absolute pressure, add atmospheric pressure: 12.445 MPa + 0.101 MPa = 12.545 MPa.

4) f = pA; A must be in m².
f = 12.545 E6 Pa × π (0.437)² m² = 7.526 E6 N.