A tank is 10 m long, 6 m wide, 3 m high, and contains kerosene with density 820 kg/m3 to a depth of 2.5 m. (Use 9.8 m/s2 for the acceleration due to gravity.) (a) Find the hydrostatic pressure on the bottom of the tank. Pa (b) Find the hydrostatic force on the bottom of the tank. N (c) Find the hydrostatic force on one end of the tank. N

a)

Pressure on the bottom

= hdg

= 2.5 x 820 x 9.8

= 20090 N / m²

b)

force = area x pressure

= 20090 x 10 x 6 N

= 1205400 N

c)

Force on 10m x 2.5 m face

center of gravity of the tank will lie at height 2.5 / 2 = 1.25 m

Pressure = hdg

= 1.25 x 820 x 9.8

= 10045 N/m²

force = pressure x area

= 10045 x 10 x 2.5

= 251125 N.

length of tank, l = 10 m

width of tank, w = 6 m

height of tank, h = 3 m

density of kerosene, d = 820 kg/m³

g = 9.8 m/s²

(a) Hydrostatic pressure

P = h' x d x g

P = 2.5 x 820 x 9.8 = 20090 Pa

(b) Force on bottom

F = Pressure x area of bottom

F = 20090 x 10 x 6

F = 1205400 N

(c) Force on arm 10 m x 2.5 m

The center of gravity of the tank = 2.5 / 2 = 1.25 m

Pressure = hdg

P = 1.25 x 820 x 9.8

P = 10045 N/m²

Force = pressure x area

F = 10045 x 10 x 2.5

F = 251125 N