(a) Using Bernoulli's equation, show that the measured fluid speed $v$ for a pitot tube, like the one in Figure 12.7$(\mathrm{b})$ is given by $v=\left(\frac{2 \rho^{\prime} g h}{\rho}\right)^{1 / 2}$ where $h$ is the height of the manometer fluid, $\rho^{\prime}$ is the density of the manometer fluid, $\rho$ is the density of the moving fluid, and $g$ is the acceleration due to gravity. (Note that $v$ is indeed proportional to the square root of $h,$ as stated in the text.) (b) Calculate $v$ for moving air if a mercury manometer's $h$ is 0.200 $\mathrm{m} .$