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Question

(D) According to the equation of continuity for an ideal fluid,the product of the cross-sectional area and the velocity of the fluid remains constant

Vedclass · Accepted Answer

$4:1$

Vedclass · Answer

(D) According to the equation of continuity for an ideal fluid,the product of the cross-sectional area and the velocity of the fluid remains constant at all points along the pipe.Therefore,$A_A v_A = A_B v_B$,where $A$ is the cross-sectional area and $v$ is the velocity.The area of a circular cross-section is given by $A = \pi r^2 = \pi (d/2)^2 = \frac{\pi d^2}{4}$,where $d$ is the diameter.Thus,$\frac{v_A}{v_B} = \frac{A_B}{A_A} = \frac{\frac{\pi (d_B)^2}{4}}{\frac{\pi (d_A)^2}{4}} = \left( \frac{d_B}{d_A} \right)^2$.Given $d_A = 5 \ cm$ and $d_B = 10 \ cm$,we have:$\frac{v_A}{v_B} = \left( \frac{10}{5} \right)^2 = (2)^2 = \frac{4}{1}$.Hence,the ratio of the velocities of the fluid at $A$ and $B$ is $4:1$.

An ideal fluid flows through a pipe of circular cross-section with diameters $5 \ cm$ and $10 \ cm$ as shown. The ratio of velocities of the fluid at $A$ and $B$ is

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