Question

question 16 (1 point)
an incompressible ideal fluid flows steadily through a pipe that has a change in diameter. the flu speed at a location where the pipe diameter is 8.0 cm is 1.28 m/s. what is the fluid speed at a location where the diameter has narrowed to 4.0 cm?

a) 0.32 m/s

b) 5.1 m/s

c) 1.3 m/s

d) 2.6 m/s

e) 0.64 m/s

Explanation:

Step1: Recall Continuity Equation

For incompressible fluid, \( A_1v_1 = A_2v_2 \), where \( A=\pi(\frac{d}{2})^2 \). So \( \pi(\frac{d_1}{2})^2v_1=\pi(\frac{d_2}{2})^2v_2 \), simplify to \( d_1^2v_1 = d_2^2v_2 \).

Step2: Identify Known Values

\( d_1 = 8.0\,\text{cm} \), \( v_1 = 1.28\,\text{m/s} \), \( d_2 = 4.0\,\text{cm} \).

Step3: Solve for \( v_2 \)

Rearrange formula: \( v_2 = v_1\times(\frac{d_1}{d_2})^2 \). Substitute values: \( v_2 = 1.28\times(\frac{8.0}{4.0})^2 = 1.28\times4 = 5.12\approx5.1\,\text{m/s} \).

Answer:

b) 5.1 m/s