To find the velocity of efflux from a hole at the bottom of a tank filled with water, we can use Torricelli's theorem. According to this principle, the velocity \( v \) of fluid flowing out of an orifice under the influence of gravity can be calculated using the formula:
Formula for Velocity of Efflux
The formula is given by:
v = √(2gh)
Where:
- g = acceleration due to gravity (approximately 9.81 m/s²)
- h = height of the fluid column above the hole
Calculating Pressure and Height
In this scenario, the total pressure at the bottom of the tank is given as three atmospheres. Since 1 atmosphere equals \( 10^5 \, \text{N/m}^2 \), we can convert this pressure:
Pressure = 3 atm = 3 × 10^5 N/m²
Using the hydrostatic pressure formula:
Pressure = ρgh
Where:
- ρ = density of water (approximately \( 1000 \, \text{kg/m}^3 \))
- h = height of the water column
Finding Height
Rearranging the formula to find height:
h = Pressure / (ρg)
Substituting the values:
h = (3 × 10^5) / (1000 × 9.81) ≈ 30.6 \, \text{m}
Calculating Velocity
Now, substituting \( h \) back into the velocity formula:
v = √(2gh) = √(2 × 9.81 × 30.6)
Calculating this gives:
v ≈ √600 \, \text{m/s}^2
Final Answer
The velocity of efflux at the bottom of the tank is approximately:
√600 m/s
Thus, the correct option is C. √600 m/s.
