Velocity ratio

Determine the ratio at which the fluid velocity in different parts of the pipeline (one piece has a diameter of 5 cm and the other has a diameter of 3 cm) when you know that every point of the liquid is the product of the area of the tube [S] and the fluid velocity [v] the same.

Final Answer:

r =  9:25

Step-by-step explanation:

$$\begin{gathered} r=v_1:v_2 \\ {d}_1=5\text{cm} \\ {d}_2=3\text{cm} \\ {S}_1=\pi (d_1/2{)}^2 \\ {S}_2=\pi (d_1/2{)}^2 \\ {Q}_1=Q_2 \\ {S}_1\cdot v_1=S_2\cdot v_2 \\ \pi (d_1/2{)}^2\cdot v_1=\pi (d_2/2{)}^2\cdot v_2 \\ {d}_1^2\cdot v_1=d_2^2\cdot v_2 \\ {v}_1:v_2=d_2^2:d_1^2 \\ r=v_1:v_2 \\ r=\frac{d_2^2}{d_1^2}=\frac{3^2}{5^2}=0.36=9:25 \end{gathered}$$

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