Consider a square gasoline tank with sides of 10 m and heigh

Consider a square gasoline tank with sides of 10 m and height of 15 m as shown in the figure Some water has penetrated the base to a depth of 10 cm. Gasoline fills up to 8 m above The rest of the tank is filled with air at 200 kPa (abs). Compute the pressure at the base of the tank? Show sour work. Compute the force on one of the walls exerted b) the air. gasoline and water. Show your work. Consider a quarter-circle gate with a thickness of I inch, a radius of 6 ft and a width of 18 ft as shown The gate is nude of steel with a specific weight of 500 lb/ft^3 Compute the hydrostatic force and locate the point 0(x_0.y_0) through which it acts referred from A. Show your work. Compute the moment at A due to the combined hydrostatic force and weight of the gate. Show your work.

Solution

1.) pressure of air (P_air) = 200kPa = 200000 Pa

speicific weight of gasoline = 6.67 kN/m³

specific weight of water = 9.8 kN/m³

Now,

pressure at the depth of the tank can be given by:

a.) Pressure at bottom of tank = pressure of air + pressure by gasoline + pressure by water

= 200 + (specific weight X height of gasoline )+ (specific wt. X height of water)

= 200 + (6.67 X 8) + (9.8 X 0.1)

= 254.34kPa

b.) Pressure = force / area

or, force = (pressure X area)_air + (pressure X area)_gasoline + (pressure X area)_water

   _{= (200 X 10 X (15-8.1)) + ([6.67 X 8] X [10 X 8] + ([9.8X0.1] X [10 X 0.1])}

= 13800 + 4268.8 + 0.98

= 18069.78kN