Water tube pressure

Water flows in a horizontal tube at a speed of 2.24 m/s and has a pressure of 0.1 MPa. How fast does the water flow in the narrowed part of the tube if its pressure is 0.09 MPa?

Final Answer:

v₂ =  5 m/s

Step-by-step explanation:

$$\begin{gathered} v_1=2.24\text{m/s} \\ {p}_1=0.1\cdot 10^6=100000\text{Pa} \\ {p}_2=0.09\cdot 10^6=90000\text{Pa} \\ \rho =1000{\text{kg/m}}^3 \\ {p}_1+\frac{1}{2}\cdot \rho \cdot v_1^2=p_2+\frac{1}{2}\cdot \rho \cdot v_2^2 \\ {p}_1-p_2+\frac{1}{2}\cdot \rho \cdot v_1^2=\frac{1}{2}\cdot \rho \cdot v_2^2 \\ 2(p_1-p_2)/\rho +v_1^2=v_2^2 \\ {v}_2=\sqrt{2\cdot (p_1-p_2)/\rho +v_1^2}=\sqrt{2\cdot (100000-90000)/1000+2.24^2}=5\text{m/s} \end{gathered}$$

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