1) The containers in the sketch contain water (density=996 kg/m 3 ) each filled

Question

1) The containers in the sketch contain water (density=996 kg/m3) each filled to a depth of 2.5 m. The pressure at the free surface is 100 kPa. For both the containers, calculate the following quantities:

a) both the absolute and gage pressure in the water at the bottom of the container.

b) gage pressure force exerted by the water on the bottom surface of the container

c) weight of the water

d) Are these results surprising( when you compare weight and pressure forces at the bottom surface)? Discuss. This is called hydrostatic paradox.

Explanation / Answer

a) Absolute pressure is 100kPa + 2.5m*996kg/m^3*9.8m/s^2 = 100 kPa + 24kPa = 124kPa gage pressure only measures pressure over atmospheric, so 24kPa. b) Pressure = force/area so pressure*area = force Container A Force = 24kPa*(.25m)^2*Pi = 4.8 kN Container B Force = 24kPa*(.5m)^2*Pi = 19.2 kN (four times the force) c) weight is the same for both Volume = (area top + area bottom)/2*height = 1.23 m^3 Weight = 1.123m^3*996 kg/m^3*9.8 m/s^2 = 11,980 N or 11.98 kN d) yes, this is surprizing. The weight is the same, but the total force is smaller than the weight on the bottom of container A and larger than the weight on the bottom of container B. In container A the walls have a component up. This pushes up on the water and the water pushes down on the walls. In container B the walls are sloped out. The water pushes on the sloped walls and there is an equal and opposite force with a component down on the water.

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