Explanation Given Info: ∇ . v → = x 2 where v → is the velocity field of the fluid. The curve is the boundary of a circle of radius 2 centred at the origin. Formula Used: Flux of a vector field F → across a boundary C enclosing the region D is given by, Flux = ∬ D ( ∇ . F → ) d A Calculation: In polar co-ordinates, x = r cos θ , y = r sin θ and d A = d x d y = r d r d θ Therefore, flow rate of the fluid = ∬ D ( ∇ . v → ) d A = ∬ D x 2 d A = ∬ D ( r cos θ ) 2 r...

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Chapter 18.1, Problem 44E

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The flow rate of a fluid across the circle of radius $2$ centred at the origin.

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Chapter 18.1, Problem 43E

Chapter 18.1, Problem 45E

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The flow rate of a fluid across the circle of radius 2 centred at the origin.

Solution Summary: The author explains that the flow rate of a fluid across the circle of radius 2 centred at the origin is 4.

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The flow rate of a fluid across the circle of radius $2$ centred at the origin.

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Chapter 18 Solutions