1. A boat has the shape of a rectangular box. The cross sectional area of the bo

Question

1.A boat has the shape of a rectangular box. The cross sectional area of the bottom of the barge 20 m^2. The total mass of the barge is 1000kg. The waterline of the barge floating in fresh water is traced on its side with a painted line. If the barge sails out in the ocean (the mass density of sea water is 1030 kg/ m^3), will the painted line be above the water or underwater? By What distance?

2. A cylindrical storage tank has a cross sectional area A1 = 1.5m^2. The tank is set up vertically on the ground and filled with V = 7.5m^3 of water. There is a valve at the bottom of the tank with an internal cross sectional area of 1.5 cm^2. What fraction of the total volume will be drained in the first 50 minutes after the valve is opened?

Explanation / Answer

1) area = 20 m2

density of fresh water = 1000 kg /m3

now to float it need to displace water equal to its weight

so height can be calculated

20 m2 * h * 1000kg /m3 = 1000kg

=> h= 1/20 m = 0.05 m

now in sea the density 1030 kg /m3

so water displaced

20 m2 * h * 1030kg /m3 = 1000kg

h= 0.0485 m

so the painted line will be above water by 0.00145 m

2) now ,

height of water in the tank = 7.5 / 1.5 = 5m

cross sectional area 1.5 cm2

the discharge rate will be given as area of oriface * sqrt ( 2g*H)= 0.00015* sqrt( 2*9.8*5) = 1.4849 x10-3 m3/s

so ,

volume discharges in 50 mins = 3000 secs= 1.4849 x10-3 m3/s * 3000 = 4.454 m3

so fraction = 4.454/7.5 = 0.59 fraction

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