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Fluids and Conservation Laws (Continuity, Bernoulli)

AP Physics 1· difficulty 2/5

A₁, v₁ A₂, v₂

Water flows through a pipe that narrows from cross-sectional area A1=0.040 m2A_1 = 0.040~\text{m}^2 (speed 2.0 m/s2.0~\text{m/s}) to A2=0.010 m2A_2 = 0.010~\text{m}^2. What is the speed in the narrow section?

  • A

    2.0 m/s2.0~\text{m/s}

  • B

    8.0 m/s8.0~\text{m/s}

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  • C

    0.5 m/s0.5~\text{m/s}

  • D

    4.0 m/s4.0~\text{m/s}

Explanation

Continuity (incompressible): A1v1=A2v2⇒v2=(0.040/0.010)(2.0)=8.0 m/sA_1 v_1 = A_2 v_2 \Rightarrow v_2 = (0.040/0.010)(2.0) = 8.0~\text{m/s}.

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