Problem 1: Equation of Continuity, Bernoulli's Equation, and Rates (a) In the figure above, show that Bernoulli's principle predicts that the level of the liquid, h = y2 - Y₁. drops at a rate V₂ = 12-1 dh dt 2ghA A-A where A, and A₂ are the areas of the opening and the top surface, respectively, assuming viscosity is ignored. (b) Determine h as a function of time by integrating. Let h ho at t = 0. (c) How long would it take to empty a 20 cm tall cylinder with 2.1 L of water if the opening is at the bottom and has a 0.50 cm diameter.
Problem 1: Equation of Continuity, Bernoulli's Equation, and Rates (a) In the figure above, show that Bernoulli's principle predicts that the level of the liquid, h = y2 - Y₁. drops at a rate V₂ = 12-1 dh dt 2ghA A-A where A, and A₂ are the areas of the opening and the top surface, respectively, assuming viscosity is ignored. (b) Determine h as a function of time by integrating. Let h ho at t = 0. (c) How long would it take to empty a 20 cm tall cylinder with 2.1 L of water if the opening is at the bottom and has a 0.50 cm diameter.
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Transcribed Image Text:Problem 1: Equation of Continuity, Bernoulli's Equation, and Rates
(a) In the figure above, show that Bernoulli's principle predicts that the level of the liquid, h = y₂ -₁,
drops at a rate
V₂ =
VE YE
dh
dt
2ghA
A-A
where A₁ and A₂ are the areas of the opening and the top surface, respectively, assuming viscosity is
ignored.
(b) Determine h as a function of time by integrating. Let h ho at t = 0.
(c) How long would it take to empty a 20 cm tall cylinder with 2.1 L of water if the opening is at the
bottom and has a 0.50 cm diameter.
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