A U-shaped pressure gauge (used to measure pressure) is initially full of water, but is exposed to a pressure difference such that the water level on its left side is 0.05 m higher than the water level on its right side. At t = 0, the pressure difference is suddenly removed. When friction is neglected, the height of the water level on the left side and measured from the central plane between the two initial water levels is given by the solution of the equation: ,d²y L' dt? -2gy

University Physics Volume 1
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Author:William Moebs, Samuel J. Ling, Jeff Sanny
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Chapter14: Fluid Mechanics
Section: Chapter Questions
Problem 129CP: Fluid originally flows through a tube at a rate of 100 cm3/s. To illustrate the sensitivity of flow...
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A U-shaped pressure gauge (used to measure pressure) is
initially full of water, but is exposed to a pressure difference
such that the water level on its left side is 0.05 m higher
than the water level on its right side. Att = 0, the pressure
difference is suddenly removed. When friction is neglected,
the height of the water level on the left side and measured
from the central plane between the two initial water levels
is given by the solution of the equation:
-2gy
dt?
where L = 0.2 m is the length total U-shaped tube, and g =
10 m / s.
a) Find the power series that represents ODE described by
the model and find the y value for 2 s.
b) Knowing that the solution analytical value of the above
ODE is y (t) = 0.5 cos (10t), show using series of McLaurin
in the cosine function, which series found in item a),
corresponds to the analytical solution
Transcribed Image Text:A U-shaped pressure gauge (used to measure pressure) is initially full of water, but is exposed to a pressure difference such that the water level on its left side is 0.05 m higher than the water level on its right side. Att = 0, the pressure difference is suddenly removed. When friction is neglected, the height of the water level on the left side and measured from the central plane between the two initial water levels is given by the solution of the equation: -2gy dt? where L = 0.2 m is the length total U-shaped tube, and g = 10 m / s. a) Find the power series that represents ODE described by the model and find the y value for 2 s. b) Knowing that the solution analytical value of the above ODE is y (t) = 0.5 cos (10t), show using series of McLaurin in the cosine function, which series found in item a), corresponds to the analytical solution
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