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g A circular swimming pool has a diameter of 10 m, the sides are 4 m high, and the depth of the water is 3 m. How much work (in Joules) is required to pump all of the water over the side

Sagot :

okpalawalter8

Answer:

[tex]W=2.69*10^{6}J[/tex]

Explanation:

Generally the equation for momentum is mathematically given by

Diameter [tex]d=10m[/tex]

Radius [tex]r =\frac{d}{2}=>5m[/tex]

Height [tex]h=4m[/tex]

Depth [tex]d=3m[/tex]

Generally the equation for Area of the circle is mathematically given by

[tex]A=\pi r^2[/tex]

[tex]A=\pi 5^2[/tex]

[tex]A=78.5m^2[/tex]

Generally the equation for Work done is mathematically given by

[tex]d_w=d_f*x[/tex]

Where

[tex]d_f=(\rho*d_v)*g[/tex]

Therefore

[tex]d_w=((\rho*d_v)*g)*x[/tex]

[tex]d_w=((1000*78.5)*9.8)*x dx[/tex]

[tex]d_w=769300x dx[/tex]

[tex]W=\int dw[/tex]

[tex]\int dw=769300 \int^4_{3}x dx[/tex]

[tex]W=(769300\2)*7[/tex]

[tex]W=2.69*10^{6}J[/tex]

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