The fluid density of honey is 1420 kg/m^3, after measuring the pressure at diffe

Question

The fluid density of honey is 1420 kg/m^3, after measuring the pressure at differnet depths it is found that the slope of all the points = 13.818 kpa/meter.

Calculate the product between the density of the fluid and the gravitational acceleration. Compare it with the slope you calculated above. What can you conclude?

Using the conclusions from above, write a mathematical expression for the pressure (as a function of depth, density and gravitational acceleration) that will allow you to calculate the pressure at any depth. (should this be pressure = depth*density*gravitational acceleration) p = h*rho*g

Using this equation calculate the pressure at a depth of 10.5m. What does this conclude about the pressure in a fluid? How does it change with depth?

Explanation / Answer

rho g = 1420*9.78 = 13.89 kPa

rho *g should equal to the slope, which is larger than the measuring slope 13.82, the measuring data have system error, or the actual density of honey is lower than given.

you need to add P0 to get absolute pressure

p = h*rho*g+ p0 = 13.82 h + 101.3 kPa

at 10.5 m,

P = 13.82 *10.5 +101.3 = 246.41 kPa

the pressure in the fluid is a linear function of the depth in the fluid.  

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