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A large tank containing a mystery liquid is filled to a depth of L = 35...

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Advance Math

A large tank containing a mystery liquid is filled to a depth ofL = 35 m. The upper surface of the liquid isexposed to the atmosphere (of density 1.2kg/m3). A pipe of cross-sectional areaAin = 0.01 m2 is inserted into the liquid. The other ’outlet’ end of the pipe, of smaller crosssectional area Aout = 0.005m2, is placed outside theliquid at a height of h = 2 m below the surface ofthe liquid. Fluid begins to flow out of the outlet.

a (7 points) Someone submerges an object of density 900kg/m3 in the mystery liquid, and it floatssuspended (a = 0). What is the density of the mystery liquid?

b (7 points) Find the speed vout of the liquidflowing out of the outlet.

c (6 points) Find the speed vin of the liquid flowinginto the pipe.

d(5points) Now a fierce wind with vwind =35m/s blows parallel to the entire surface of the tankexposed to the air (it does not reach or affect the air around theoutlet). This lowers the pressure on the liquid at the top of thetank (but liquid does not spill over the top). With the windblowing, how much slower is the liquid flowing out of theoutlet?

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