Answer:
Step-by-step explanation:
Given a rectangular tank with dimension (10ft by 20ft by 16ft)
Then the volume of the tank is
Volume =length × breadth ×height
Volume=10×20×16=3200ft³
V=3200ft³
Then,
∆F= weight density × volume
∆F= 62.4×3200
∆F= 199,680 lb
Then,
Let the 0-point on the x-axis be at the bottom of the tank, so the level of the water ranges from x = 0 to x = 16ft. (It would just as well to let 0 be ground level and let x range from x = −26ft to x − 0.) Then a slice of water at level x is raised (26− x)ft
Then ∆x=(26-x)ft
Work is given as
W= -∫F∆xdx. From 0 to 16
W= -∫199,680(26-x)dx From 0 to 16
W=-199,680∫26-x dx From 0 to 16
W=-199,680 (26x-x²/2). From 0 to 16
W=-199,680(26×16-0.5×16² -0-0)
W=-199,680(288)
W=-57,507,840J
The work done to empty the tank is 57,507,840J
