A small closed bottle is filled with water to adepth of 30 cm .A small hole located 10 cm above the bottom of the bottle is then opened .What is the speed of the water emerge from the hole in m\sec unit
h=0.30 m, hₒ=0.10 m.
Bernoulli’s equation between the top surface and the exitting stream:
Pₒ+0+ρghₒ=Pₒ+ρv²/2+ ρgh,
v² = 2g(hₒ-h),
v=sqrt{2g(hₒ-h)}=sqrt{2•9.8•(0.30-0.10)} =
To answer this question, we can use Torricelli's law, which relates the speed of efflux (the speed at which a fluid emerges from a small hole) to the height of the fluid above the hole.
Torricelli's law states that the speed of efflux is given by the equation:
v = √(2gh)
Where:
v = speed of efflux
g = acceleration due to gravity (approximately equal to 9.8 m/s^2)
h = height of the fluid above the hole
In this case, the height of the fluid above the hole is 10 cm, or 0.1 meters. Plugging this value into the equation, we can calculate the speed of the water emerging from the hole.
v = √(2 * 9.8 * 0.1)
v = √(1.96)
v ≈ 1.4 m/s
Therefore, the speed of the water emerging from the hole is approximately 1.4 m/s.