A rectangular trough, 2.0 m long, 0.50 m wide, and 0.50 m deep, is completely full of water. One end of the trough has a small drain plug right at the bottom edge.
When you pull the plug, at what speed does water emerge from the hole? (in m/s)
V = sqrt (2 g H), where H is the height of the water level abouve the hole. The area of the trough does not matter.
Thank you
yw
To find the speed at which water emerges from the hole in the trough, we can use Torricelli's law, also known as Torricelli's theorem. This law states that the speed at which a fluid (in this case, water) exits a hole is equal to the square root of two times the acceleration due to gravity (g) times the height of the water column above the hole.
In this case, the height of the water column can be determined by subtracting the depth of the trough from its total length. So, the height of the water column above the hole is 2.0 m - 0.50 m = 1.50 m.
Now, we need to substitute this value into the formula:
Speed = √(2 × g × height)
The acceleration due to gravity, g, can be approximated as 9.8 m/s².
Plugging in the values:
Speed = √(2 × 9.8 m/s² × 1.50 m)
= √(29.4 m²/s²)
= 5.42 m/s (rounded to two decimal places)
Therefore, the speed at which water will emerge from the hole in the trough is approximately 5.42 m/s.