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Fluids and Conservation Laws (Continuity, Bernoulli)

AP Physics 1· difficulty 4/5

Water flows through a horizontal pipe that narrows from radius 4.0 cm to 2.0 cm. If the speed in the wide section is 1.0 m/s, the speed in the narrow section is

  • A

    16 m/s

  • B

    4.0 m/s (A1v1=A2v2A_1 v_1 = A_2 v_2, v2=v1(r1/r2)2v_2 = v_1 (r_1/r_2)^2)

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  • C

    0.50 m/s

  • D

    2.0 m/s

Explanation

Continuity: A1v1=A2v2A_1 v_1 = A_2 v_2. A∝r2A \propto r^2, so v2=v1(r1/r2)2=1.0⋅4=4.0v_2 = v_1 (r_1/r_2)^2 = 1.0 \cdot 4 = 4.0 m/s.

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