Water flows through the pipe shown Figure $1.$ Determine the following for each of the flowing cases:

i$.$ The velocity at $C$ if the velocity at $A$ is $4\frac{m}{s}$ and the velocity at $B$ is $6\frac{m}{s}$

ii$.$ The velocity at $B$ if the velocity at $A$ is $6\frac{m}{s}$ and the velocity at $C$ is $4\frac{m}{s}$

iii. The velocity at $C$ if the mass flow rate at $A$ is $50k\frac{g}{s}$ and the velocity at $B$ is $5\frac{m}{s}$

iv$.$ The velocity at $C$ if the mass flow rate at $A$ is $50k\frac{g}{s}$ and the mass flow rate at $B30k\frac{g}{s}$

Figure $1$