A common way to perform work below the surface of a river is to sink a large, op

Question

A common way to perform work below the surface of a river is to sink a large, opened ended box (i.e., caisson) to the bottom of the work area, then use an air pump on the surface to push the water out of the caisson. Assuming a) an air density of 1.2 kg/m^3 and an atmospheric pressure of 101 kPa at the surface of the river and b) a water density of 988 kg/m^3 in the river, what would be the gage pressure in the caisson, if the open ended bottom of the caisson is 50m below the surface of the river? How would the gage pressure change if the air temperature decreased several degree C? How would the gage pressure change if the water temperature increased several degree C? Which temperature change (i.e., air vs water) would affect the gage pressure more per degree C?

Explanation / Answer

(1) Apply bernoullis between two point Considering air as incompressible as the atmospheric condition is constant
P1/pairg + h = P2/pwaterg
Where P2 is absolute pressure if we check gausge pressure then P1 = 0
and Gauge pressure at 2 i.e P2 = pwater*gh = 1000*9.81*50 = 4.905 bar
(2) When the temperature changes the density of air changes
therefore
the pressure at the point 2 will change from equation 1
We know that
Density (p) = P/RT where P is the pressure and T is the temperature
So on increasing the tempearature density decreases.
therefore the pressure at point 2 will increase.
(3) On decreasing the temperature the denstiy will increase therfore the pressure will decrease.
(4) Change in air temperature would affect more than water because air density changes to rapidly with temperature.

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