- #1
tsumi
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Homework Statement
A tank of height h full of water with it's base 40 meters from the ground, with a hole on the lateral wall at the base. The water comes out of the tank at 6.93 m/s to fill a pool on the ground. The water hits the center of the pool at a distance of 19.5 meters measured horizontally from the tank. What is the tank height h? You can despise the variation of height of the tank while it is being unfilled.
Homework Equations
Continuity: A₁v₁=A₂v₂
Bernoulli: P + 1/2ρv² + ρgh = Cte
free fall of the water (previously calculated): y(t)= 40 -4.9t²
x(t)= 6.93t
The Attempt at a Solution
I used Bernoulli equation, considering that the point at which the water leaves the tank as a pressure P, is at h=40, and as a speed v=6.93, and the point at which the water reaches the floor as a pressure P₀ (1 atm = 1.013×10⁵), h=0 and v=28.843(calculated using the law motion of the water in free fall and doing the norm of two velocities: √(V²x + V²y) ).
With this I would find the pressure P, then I would do: P = P₀ + ρgh <=> h = (P-P₀)/(ρg).
But this way the pressure P results lower than the atmospheric pressure P₀, which make things impossible... what I think I was missing is the fact that as speed increases while the water falls, the pressure decreases.. so the value of the pressure when the water hits the floor must be lower than P₀, but I can't solve the problem this way =\
I would really apreciate some help thanks ^^