The density ρ of a fluid changes proportionally with depth from the surface h according to the following formula: ρ(h) = ρ0 + ch. where ρ0 is the density of the fluid at the surface (h = 0), and c is a constant. a)Write an expression for the gauge pressure p as a function of the depth. b)A pressure gauge is placed at a depth of 6.3 m in a fluid with density that varies with depth as described above. The constant c is 720 kg/m4. The density of the fluid at h = 0 is 0 kg/m4. What pressure, in pascals, would the gauge read?
Fluid Pressure
The term fluid pressure is coined as, the measurement of the force per unit area of a given surface of a closed container. It is a branch of physics that helps to study the properties of fluid under various conditions of force.
Gauge Pressure
Pressure is the physical force acting per unit area on a body; the applied force is perpendicular to the surface of the object per unit area. The air around us at sea level exerts a pressure (atmospheric pressure) of about 14.7 psi but this doesn’t seem to bother anyone as the bodily fluids are constantly pushing outwards with the same force but if one swims down into the ocean a few feet below the surface one can notice the difference, there is increased pressure on the eardrum, this is due to an increase in hydrostatic pressure.
The density ρ of a fluid changes proportionally with depth from the surface h according to the following formula: ρ(h) = ρ0 + ch. where ρ0 is the density of the fluid at the surface (h = 0), and c is a constant.
a)Write an expression for the gauge pressure p as a function of the depth.
b)A pressure gauge is placed at a depth of 6.3 m in a fluid with density that varies with depth as described above. The constant c is 720 kg/m4. The density of the fluid at h = 0 is 0 kg/m4. What pressure, in pascals, would the gauge read?
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