Staility – I : Chapter 2

5. A rectangular lock gate 36m wide and 20m high has FW on one side to a depth of 16m. Find what depth of SW on the other side will equalize the thrust.

Solution : Inside the lock gate area =( 36 x 16)m2

Pressure = depth x density =(16/2 x 1)
                                                      = 8 t/m²

Thrust inside the lock gate = (pressure x area)
Thrust =(8 x 36 x 16)
       = 4608 t

Let ‘X’ depth of   salt water on other side will equalize the thrust .

Pressure     = depth x density =( X/2 x 1.025)
Area    =(36 x  X )
Thrust = (P x A)

4608 = (X/2 x 1.025 x 36X )
4608 = (1.025 x 36X  x  X/2)
4608 =   (1.025 x 36X²/2)
           =   ( 1.025 x 18X²)
X²   = (4608 /1.025 x 18)

X = 15.8 m

Hence, Depth of other side of lockgate =15.8m