Question

3500kg of water are poured into a water tank and fill a volume equal to 3.5m^3. a. What is the density of the water?

b. If the height of the water is 150 cm what is the gauge and total pressures at the bottom of the tank?
c. An object with a density of 40kg/m^3 and volume of 55cm^3 us submerged in the water tank and tethered by a string to the bottom surface. what is the buoyant force acting on the object?

Answer 1

a )

Density = mass / volume

= 3500 / 3.5

= 1000 kg m⁻³

b) gauge pressure = h d g

h is height of water column

d is density

g is acceleration due to gravity

Put the values in the equation above

Gauge pressure = .15 x 1000 x 9.8

= 1470 Nm⁻²

Atmospheric pressure = 100000 Nm⁻²

Total pressure

= 101470 N m⁻²

c ) Volume of water displaced = volume of object

= 55 x 10⁻⁶ m³

Buoyant Force = weight of displaced water

= 55 x 10⁻⁶ x 1000 x 9.8

= .539 N.