We will have the following:
We will have that the flowrate of the water will be equal to the speed of flow multiplied by the area of flow, that is:
[tex]F=v\cdot A=v\cdot\pi r^2[/tex]In this particular case the flowrate remains constant under a given pressise, so:
[tex]v_1\cdot r^2_1=v_2\cdot r^2_2[/tex]That is:
[tex](1m/s)(r^2_1)=v_2\cdot(\frac{r_1}{4})^2[/tex]From this we can see that the value of the speed in the narrower diamter is expected to increase, So:
[tex](1m/s)\cdot r^2_1=v_2\cdot\frac{r^2_1}{16}\Rightarrow1m/s=v_2\cdot\frac{1}{16}[/tex][tex]\Rightarrow v_2=16m/s[/tex]So, the velocity will be 16 m/s.
