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

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$v$

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(B) According to the equation of continuity for an incompressible fluid, the product of the cross-sectional area and the velocity of the fluid remains constant at all points along the flow: $A_A v_A = A_B v_B$ Given that the pipe is cylindrical, the cross-sectional area $A = \pi r^2$. At point $A$, the radius is $2R$, so $A_A = \pi (2R)^2 = 4\pi R^2$. At point $B$, the radius is $R$, so $A_B = \pi R^2$. The velocity at point $B$ is given as $v_B = 4v$. Substituting these values into the continuity equation: $4\pi R^2 	imes v_A = \pi R^2 	imes 4v$ Dividing both sides by $4\pi R^2$: $v_A = v$

$A$ liquid flows steadily through a cylindrical pipe having a radius $2R$ at point $A$ and radius $R$ at point $B$ farther along the flow direction. If the velocity at point $B$ is $4v$, what will be the velocity at point $A$?

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