This study examines the potential for fault-tolerant quantum computers to provide utility in fluid-dynamics simulations, with a focus on drag-force calculations for ship-hull design. We assess whether quantum algorithms can surpass classical computational limits by generating detailed quantum resource estimates (QREs) in terms of logical qubits and T-gate counts. Our analysis is based on a quantum algorithm leveraging Carleman linearization of the lattice Boltzmann method (LBM), which has been suggested to offer exponential speedup. We develop efficient block encodings for LBM matrices and a method for amplitude-encoding drag force. We apply the method to the simple case of fluid flow past a sphere across a range of Reynolds numbers (Re). We estimate the required (logicalqubits) × (T − gates), finding them to be prohibitively large, ranging from 1021 to 1039. While classical simulations scale as O(Re3), our QREs exhibit a modest polynomial scaling of O(Re2.68), indicating no exponential quantum advantage. We attribute this limitation to an intrinsic power-law relationship between spatial-grid resolution and time-stepping requirements that is a fundamental characteristic of explicit methods for evolving nonlinear differential equations. Thus, quantum computers are unlikely to

provide utility in applications that require time-evolving fluids and other systems of nonlinear differential equations.