LAQ : What are the pressure and total thrust on the bottom of a cylindrical vessel of diameter 0.28 m containing 30.8 litres of mercury?

Question

What are the pressure and total thrust on the bottom of a cylindrical vessel of diameter 0.28 m containing 30.8 litres of mercury? (density of mercury = 13.6 × 10³ Kg/m³) [Ans. 66.64 × 10³ N/m², 4.1 × 10³ N]

Answer

Diameter (d) = 0.28 m

Volume (V) = 30.8 L = 0.0308 m³

Step 1: Calculation of Area of base

Area = πr²

= 22\over 7 × 0.14²

= 0.0616 m²

Step 2: Calculation of Thrust

Thrust (F) = Mass × g

= Volume × density × g

= 0.0308 × 13.6 × 10³ × 10

= 4100 N

Step 3: Calculation of Pressure

Pressure (P) = Thrust\over Area

= 4100\over 0.0616

= 66558.44 Pa or 6.65 × 10⁴ Pa