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Fluids and Conservation Laws (Continuity, Bernoulli)

AP Physics 1· difficulty 2/5

r₁ = 4 cm r₂ = 2 cm

Water flows through a pipe whose radius drops from r1=4 cmr_1 = 4~\text{cm} to r2=2 cmr_2 = 2~\text{cm}. If the speed in the wide section is 1.0 m/s1.0~\text{m/s}, the speed in the narrow section is

  • A

    0.25 m/s0.25~\text{m/s}

  • B

    4.0 m/s4.0~\text{m/s}

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  • C

    0.50 m/s0.50~\text{m/s}

  • D

    2.0 m/s2.0~\text{m/s}

Explanation

Continuity: A1v1=A2v2A_1 v_1 = A_2 v_2, with A∝r2A \propto r^2: v2=(r1/r2)2v1=4⋅1.0=4.0 m/sv_2 = (r_1/r_2)^2 v_1 = 4 \cdot 1.0 = 4.0~\text{m/s}.

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