How to Empty a Tank Using Bernoulli's Equation

How can we determine the time it takes to empty a tank using Bernoulli's equation?

If a 1-m diameter cylindrical tank initially contains liquid fuel and has a 2-cm rubber plug at the bottom, as shown in Fig, how long will it take to empty the tank? The initial height of liquid in the tank is 1.5 m. Bernoulli's equation is required.

Answer:

It will take approximately 202.7 seconds to empty the tank.

Using Bernoulli's equation, we can determine the time it takes to empty a tank by considering the sum of pressure, kinetic energy, and potential energy per unit volume constant along a streamline for an ideal fluid.

The equation is expressed as P + 0.5ρv^2 + ρgh = constant, where P is pressure, ρ is density, v is velocity, g is gravitational acceleration, and h is height.

Initially, the tank contains liquid with a height of 1.5 m. The pressure at the bottom of the tank can be considered atmospheric (P = Patm) since the tank is open. At the bottom, the velocity of the liquid exiting the tank can be calculated using v = sqrt(2gh), where g is the acceleration due to gravity (9.81 m/s²) and h is the initial height (1.5 m).

By using this equation and the given data, we can determine that it will take approximately 202.7 seconds to empty the tank.