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Delgadojacky0206
25.09.2020 •
Physics
An rectangular tank 5 m long, 2 m wide, and 8 m high is filled to a depth of 5 m of water. Set up the integral that would compute the work needed to pump the water out of a spout located at the top of the tank. Use the location of the origin and the direction of the positive axis as specified in the different parts. Note: Do not input values for the constant p9
(A) The origin is at the top of the tank with with positive y-values going down pg dy
(B) The origin is at the bottom of the tank with positive y-values going up. pg dy
(C) The origin is at the water level of the tank with positive y-values going down.dy
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Ответ:
Solution:
Given data:
A rectangular tank with dimensions 5 m as length, wide of 2 m and height of 8 m is filled with water tot a depth of 5 m.
A). If we select an elemental part of the tank of thickness dy at a depth y from the top, its mass will be :
m = p.v
⇒ m = p.(Ady)
⇒ m = p.( 5 x 2 dy)
⇒ m = 10 p dy
Now work done in moving mass from a depth y to the top will,
dw = m.g.y
dw = (10 p dy).g.y
or dw = 10 p.g.y.dy
Total work done is :
W = 300 p.g
B). Origin at the bottom and consider an elemental part of the tank at a height y from the bottom, then its mass is :
⇒ m = p.( 5 x 2 dy)
⇒ m = 10 p dy
Now, work done in moving this mass from a height y above origin to a height 8 m above the origin is,
dw = mg(8 - y)
dw = (10 p dy).g.(8 - y)
dw = 10 pg.(8 - y). dy
The total work done is
W = 10 pg (40-12.5)
W = 275 pg
C). Origin at the water level and consider y axis positive in the downward direction.
The work done to move and elemental ,as from a depth y below the water level to the top of the tank is,
dw = 10 pg (y+2) dy
The total work done is :
W = 10 p g (12.5 + 10)
W = 225 pg
Ответ: