network, total flow

Show that if a network $N$ contains no directed path from the source $s$ to the sink $t$, then the maximum possible total flow on $N$ (for any flow function) is $0$.

I am not sure how to prove this. I know I want to use the max flow min cut theorem that would show that the value of a maximum flow and the capacity of a minimum cut are both zero. So, I need some help with this one. Thanks in advance.