The pipes cross sectional area then narrows to 5 cm^2 further downstream.
This problem requires the continuity equation to determine the speed of water in the narrower section:
A1*v1 = A2*v2
A1 = 10 cm^2 and A2 = 5 cm^2
v1 = 34 cm/s and v2 has to be determined:
10*34 = 5*v2
v2 = 10*34/5
v2 = 68 cm/s
The speed of water in the narrower section of the pipe is v2 = 68 cm/s.