A plastic tube with radius $\backslash ($ R$=1\backslash$mathrm$\{$~cm$\}\backslash )$ is placed at the bottom of a well on a hill slope. The second end of the tube is located close to a large bucket $($capacity $200$ liters $\backslash (=0\mathrm{.}2\backslash$mathrm$\{$~m$\}3\backslash )).$ Once the syphone is primed $($the tube is filled with water$),$ the second end of the tube is inserted into a large bucket located downhill. The distance between the level of the water in the well and the level of the water in the bucket is $\backslash (\backslash$mathrm$\{$y$\}=2\backslash$mathrm$\{$~m$\}\backslash ).$ The distance between the level of the water in the well and the top of the tube is $\backslash ($ h$=7\backslash$mathrm$\{$~m$\}\backslash ).$

a$.$ What is the velocity of the water at the end of the pipe?

b$.$ If the distance h gets increased $($for example, by raising the top of the tube C $)$ at some point the syphon will stop working. For what value of $\backslash ($ h $\backslash )$ does the syphon stop working?