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krystinayagel013
04.01.2021 •
Physics
A cylindrical tank of radius R, filled to the top with a liquid, has a small hole in the side, of radius r, at distance d below the surface. Find an expression for the volume flow rate Q through the hole. Do not leave in terms of velocities, only leave in terms of r, R and d.
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Ответ:
Explanation:
v₁ , v₂ be velocity of flow of water at the surface and hole , h₁ and h₂ be height of surface and hole , P₁ and P₂ be pressure at surface and hole .
Using Bernoulli's formula for flow of liquid in tank
1/2 ρ v₁² + ρgh₁ + P₁ = 1/2 ρ v₂² + ρgh₂ + P₂
P₁ = P₂
1/2 ρ v₁² + ρgh₁ = 1/2 ρ v₂² + ρgh₂
1/2 ( v₁² - v₂² ) = g(h₂ -h₁ )
v₁² - v₂² = - 2gd
a₁ v₁ = a₂ v₂
π R² v₁ = π r² v₂
v₁ = r² v₂ / R²
v₁² - v₂² = -2gd
r⁴ v₂² / R⁴ - v₂² = -2gd
v₂² ( R⁴ - r⁴ ) = 2gd R⁴
v₂² = 2gd R⁴ / ( R⁴ - r⁴ )
v₂ = √ [ 2gd R⁴ / ( R⁴ - r⁴ ) ]
Ответ:
D. Cars have the same velocity at one instant of time between dots 4 and 5.
Explanation:
The two cars will eventually have the same velocity and it occurs between 4 and 5. Velocity is normally defined as displacement over time. This shows that a change in the value of either time or displacement will affect the value of the velocity. Thus, at a given time between the points 4 and 5, the two cars have the same value of velocity.