A cylindrical tank, shown in the figure, has height 8 m and radius 4 m. Suppose the water tank is half-full of water. Determine the work required to empty the tank by pumping the water to a level 6 m above the top of the tank. Use 1000 kg/m³ for the density of water and 9.8 m/s² for the acceleration due to gravity. C D 8 m 4 m Draw a y-axis in the vertical direction (parallel to gravity) and choose the center of the bottom of the tank as the origin. For 0 ≤ y ≤8, find the cross-sectional area A(y). A(y) = (Type an exact answer, using as needed.)
A cylindrical tank, shown in the figure, has height 8 m and radius 4 m. Suppose the water tank is half-full of water. Determine the work required to empty the tank by pumping the water to a level 6 m above the top of the tank. Use 1000 kg/m³ for the density of water and 9.8 m/s² for the acceleration due to gravity. C D 8 m 4 m Draw a y-axis in the vertical direction (parallel to gravity) and choose the center of the bottom of the tank as the origin. For 0 ≤ y ≤8, find the cross-sectional area A(y). A(y) = (Type an exact answer, using as needed.)
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![A cylindrical tank, shown in the figure, has height 8 m and radius 4 m. Suppose the water tank is half-full of water. Determine the work required to
empty the tank by pumping the water to a level 6 m above the top of the tank. Use 1000 kg/m³ for the density of water and 9.8 m/s² for the
acceleration due to gravity.
4 m
Draw a y-axis in the vertical direction (parallel to gravity) and choose the center of the bottom of the tank as the origin. For 0 ≤ y ≤8, find the cross-sectional area A(y).
A(y) = (Type an exact answer, using as needed.)
8 m](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5f1b7c10-7ca4-413c-bb43-fe1a15020101%2Fea94e3f0-3881-47ba-8378-8d7bcb922a79%2Friyydoe_processed.png&w=3840&q=75)
Transcribed Image Text:A cylindrical tank, shown in the figure, has height 8 m and radius 4 m. Suppose the water tank is half-full of water. Determine the work required to
empty the tank by pumping the water to a level 6 m above the top of the tank. Use 1000 kg/m³ for the density of water and 9.8 m/s² for the
acceleration due to gravity.
4 m
Draw a y-axis in the vertical direction (parallel to gravity) and choose the center of the bottom of the tank as the origin. For 0 ≤ y ≤8, find the cross-sectional area A(y).
A(y) = (Type an exact answer, using as needed.)
8 m
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Step 1: Know the concept:
VIEWStep 2: Draw a diagram of the situation:
VIEWStep 3: Derive the expression for the infinitesimal mass:
VIEWStep 4: Write the expression for the work required to bring infinitesimal mass to point P:
VIEWStep 5: Find the expression for the total work done to pump the liquid to point P:
VIEWStep 6: Calculate the required work:
VIEWStep 7: Calculate the cross-sectional area of cylinder:
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