  Across industries, traditional design and engineering workflows are being
upgraded to simulation-driven processes. Many workflows include computational
fluid dynamics (CFD). Simulations of turbulent flow are notorious for high
compute costs and reliance on approximate methods that compromise accuracy.
Improvements in the speed and accuracy of CFD calculations would potentially
reduce design workflow costs by reducing computational costs and eliminating
the need for experimental testing. This study explores the feasibility of using
fault-tolerant quantum computers to improve the speed and accuracy of CFD
simulations in the incompressible or weakly compressible regime. For the
example of simulation-driven ship design, we consider simulations for
calculating the drag force in steady-state flows, and provide analysis on
economic utility and classical hardness. As a waypoint toward assessing the
feasibility of our chosen quantum approach, we estimate the quantum resources
required for the simpler case of drag force on a sphere. We estimate the
product of logical qubits $\times$ $T$ gates to range from $10^{22}$ to
$10^{28}$. These high initial estimates suggest that future quantum computers
are unlikely to provide utility for incompressible CFD applications unless
significant algorithmic advancements or alternative quantum approaches are
developed. Encouraged by applications in quantum chemistry that have realized
orders-of-magnitude improvements as they matured, we identify the most
promising next steps for quantum resource reduction as we work to scale up our
estimates from spheres to utility-scale problems with more complex geometry.
