Final answer:
The rate of escape of water from the tank is 26.87 m/s.
Step-by-step explanation:
To calculate the rate of escape of water from the tank, we can use Bernoulli's Principle. According to Bernoulli's Principle, the total energy at any point in a fluid is constant. This principle can be expressed as:
P + 1/2 * ρ * v^2 + ρ * g * h = constant
Where P is the pressure, ρ is the density of the fluid, v is the velocity of the fluid, g is the acceleration due to gravity, and h is the height of the fluid above the reference point.
In this case, the pressure at the top of the water tank is increased by 50 kPa. Using this information, we can calculate the rate of escape of water:
- Convert the pressure increase to Pascals: 50 kPa = 50,000 Pa
- Calculate the velocity of the water at the bottom of the tank using the given information: v = 30 m/s
- Calculate the density of water using its known value: ρ = 1000 kg/m^3
- Calculate the height of the water above the reference point: h = 4 m
- Substitute the values into Bernoulli's Principal equation and solve for the velocity of the escaping water:
50,000 + 1/2 * (1000) * (v^2) + (1000) * (9.8) * (4) = 0 + 1/2 * (1000) * (30^2) + (1000) * (9.8) * (0)
50,000 + 500v^2 + 39,200 = 0 + 450,000 + 0
500v^2 = 360,000
v^2 = 720
v ≈ 26.87 m/s
Therefore, the rate of escape of water is approximately 26.87 m/s.