1. **Problem statement:** Calculate the height difference $h$ in a manometer connected to a pipe where fluid flows at velocity $v = 2.0$ m/s. The fluid has specific gravity $SG = 2.0$, and the upper portion of the manometer contains air. 2. **Relevant formula:** The pitot tube measures the dynamic pressure, which relates velocity and pressure head by Bernoulli's equation: $$h = \frac{v^2}{2g} \times SG$$ where $g = 9.81$ m/s² is acceleration due to gravity. 3. **Explanation:** - The dynamic pressure head is $\frac{v^2}{2g}$. - The specific gravity $SG$ scales the pressure head because the manometer fluid is denser than water. 4. **Calculate dynamic pressure head:** $$\frac{v^2}{2g} = \frac{(2.0)^2}{2 \times 9.81} = \frac{4.0}{19.62} \approx 0.204$$ 5. **Calculate height difference $h$:** $$h = 0.204 \times 2.0 = 0.408 \text{ m}$$ 6. **Final answer:** The height difference $h$ is approximately $0.40$ m. Thus, the correct choice is C 0.40.