A submarine moves horizontally in sea and has its axis 15m below the surface of water. A pitot tube properly placed just in front of the submarine and along its axis is connected to the 2 limbs of U-tube containing mercury. The difference in mercury level is found to be 170mm. Find the speed of the submarine knowing that the specific gravity of mercury is 13.6 and that of sea water is 1.026 with respect of fresh water.

 A submarine moves horizontally in sea and has its axis 15m below the surface of water. A pitot tube properly placed just in front of the submarine and along its axis is connected to the 2 limbs of U-tube containing mercury. The difference in mercury level is found to be 170mm. Find the speed of the submarine knowing that the specific gravity of mercury is 13.6 and that of sea water is 1.026 with respect of fresh water. 

Solution: 

Difference of Hg level, x=170mm=0,17m 

Specific gravity of Hg, sh=13.6 

Specific gravity of sea water (in pipe) sp=1.026 

h=x [(sh/ sp)-1] =[(13.6/1.026)-1]=2.0834m

 v=√2gh=√2*9.81*2.0834=6.393 m/s 

speed of submarine,v =6.393*60*60/1000 km/hr 

 v =23.01 km/hr