Attend containing water has an opening on one of its vertical walls if the centre of the opening is 20 m bell on a surface level of water in the tank calculate the velocity of the water flowing out of the opening
To calculate the velocity of the water flowing out of the opening, we can use the principle of conservation of energy.
The potential energy of the water at the surface level in the tank is given by:
PE = m * g * h,
where m is the mass of the water, g is the acceleration due to gravity, and h is the height of the center of the opening above the surface level.
The kinetic energy of the water as it flows out of the opening is given by:
KE = 0.5 * m * v^2,
where v is the velocity of the water flowing out of the opening.
According to the principle of conservation of energy, the potential energy at the surface level (PE) is converted into kinetic energy as the water flows out of the opening (KE).
Therefore, we can equate the two equations:
m * g * h = 0.5 * m * v^2.
The mass of the water cancels out, giving us:
g * h = 0.5 * v^2.
Rearranging the equation, we have:
v^2 = 2 * g * h.
Taking the square root of both sides, we get:
v = √(2 * g * h).
Now we can plug in the values:
g ≈ 9.8 m/s² (acceleration due to gravity)
h = 20 m (height of the center of the opening above the surface level)
v = √(2 * 9.8 * 20) ≈ √(392) ≈ 19.80 m/s.
Therefore, the velocity of the water flowing out of the opening is approximately 19.80 m/s.