Final answer:
To calculate the velocity of efflux from a hole at the bottom of a tank filled with water, we can use Torricelli's law. By finding the depth of the hole and using Torricelli's law, we can calculate the velocity of efflux. From the given options, none of them are the correct answer.
Step-by-step explanation:
To determine the velocity of efflux from a hole at the bottom of a tank filled with water, we can use Torricelli's law. Torricelli's law states that the velocity of efflux can be calculated using the equation v = sqrt(2gh), where v is the velocity of efflux, g is the acceleration due to gravity, and h is the depth of the hole.
Given that the total pressure at the bottom of the tank is 3 atm, we can convert this pressure to pressure in pascals by multiplying it by 105 N/m². The pressure at the hole will be equal to the pressure at the bottom of the tank plus the pressure due to the column of water above it. Using the equation P = ρgh, where P is the pressure, ρ is the density of water, g is the acceleration due to gravity, and h is the depth, we can calculate the depth of the hole.
Once we have the depth, we can substitute it into Torricelli's law to find the velocity of efflux. Given that the area of the hole is √3/2 times the cross-sectional area of the container, we can calculate the flow rate (m³/s) of the water using the equation Q = Av, where Q is the flow rate, A is the area of the hole, and v is the velocity of efflux. Finally, we can convert the flow rate to m³/s by multiplying it by 1000.