Pressure and Fluids

 A gas sample is confined in a chamber with a piston. A small load is put on the piston. If the total weight of piston and load is 36 N and the piston has an area of 2*10^-3 m^2, what is the pressure exerted on the piston by the gas?  Note: atm = * 10 ^5

 P = W total / A + atm  = 36 / 2*10^ *10^5  = or 1.3 * 10 ^5 Pa

 A column of water of height 60 cm supports a column of an unknown liquid that is 24 cm height. The density of water is 1 * 10 ^3 kg/m^3. Determine the density of the unknown liquid

 P water = p unknown  Mass density * g * h + atm = Mass density * g * h + atm  Atm and gravity are same for both and cancell  Mass density * h = mass density * h  1 * 10 ^3 * 60 = 24 * mass density  Mass density of unknown = r 2.5 *10 ^3 kg/m^3

 A barber raises his customer’s chair by applying a force of 150N to a hydraulic piston of area 0.01 m 2. If the chair is attached to a piston of area 0.1 m 2, how massive a customer can the chair raise? Assume the chair itself has a mass of 5 kg.

 To solve this problem, first determine the force applied to the larger piston.  F2 = F1 ( A2 / A1)  Pascal's principle  150 (.10 /.01) = 1500N  F=ma  1500/9.81 = m = 153 kg -5 kg for chair = 148 kg

 A ball of mass 2 kg having diameter of 50 cm falls in the swimming pool. Calculate its buoyant force and volume of water displaced.

 Given: Mass of water, m = 2 kg, Diameter of ball, d = 0.5 m r = 0.25 m  Volume of sphere = 4/3 pie r^3 =.0208 m^3  Density= mass /volume = 2 /.0208 = 96 kg/m^3  F=mg = 2*9.81 = 19.6 N  Archimedes formula = F= mass density *g*v displaced  V displaced = F/ pg = 19.6 / 96 *9.81 =.0208 m^3