The correct answer is $\boxed{\frac{1}{2}}$.
The average velocity of a fluid in a pipe is the total volume of fluid flowing through the pipe divided by the cross-sectional area of the pipe. The maximum velocity of a fluid in a pipe is the velocity of the fluid at the center of the pipe.
For steady laminar flow in circular pipes, the ratio of average velocity to maximum velocity is $\frac{1}{2}$. This can be derived from the Hagen-Poiseuille equation, which states that the volumetric flow rate of a fluid in a pipe is proportional to the pressure difference across the pipe and the fourth power of the radius of the pipe, and inversely proportional to the viscosity of the fluid.
The Hagen-Poiseuille equation can be rearranged to express the average velocity of the fluid in a pipe as follows:
$$v_a = \frac{Q}{A} = \frac{P_1 – P_2}{8\mu L}$$
where $v_a$ is the average velocity of the fluid, $Q$ is the volumetric flow rate of the fluid, $A$ is the cross-sectional area of the pipe, $P_1$ is the pressure at the inlet of the pipe, $P_2$ is the pressure at the outlet of the pipe, $\mu$ is the viscosity of the fluid, and $L$ is the length of the pipe.
The maximum velocity of the fluid in a pipe is equal to the average velocity of the fluid divided by the factor $\frac{1}{2}$. This can be derived from the following equation:
$$v_m = \frac{v_a}{2} = \frac{Q}{A} \cdot \frac{1}{2} = \frac{P_1 – P_2}{16\mu L}$$
Therefore, the ratio of average velocity to maximum velocity for steady laminar flow in circular pipes is $\frac{1}{2}$.