Answer
a. Laminar
b. Turbulent
Work Step by Step
a. Calculate the Reynolds number.
$$R=\frac{2(0.35m/s)(0.008 m)(1.05 \times 10^3 kg/m^3)}{4 \times 10^{-3}Pa \cdot s}=1470$$
This is less than about 2000, the onset of turbulence.
b. If the speed doubles, so will the Reynolds number, so the flow is turbulent.