<p>Quantum linear equation solvers generate a solution vector that sits in a subspace of the quantum computer’s larger state space. Accessing the solution vector relies on applying measurement projectors that remove components in the orthogonal subspace. This study examines the probability that the projectors are successful and how the success probability is influenced by the properties of the linear system, e.g., the matrix condition number, and approximations made in the quantum solver. The analysis is performed within a non-linear computational fluid dynamics code where, at each iteration, a linearised system is passed to an emulated quantum solver. The linear systems are solved using quantum singular value transformation, for which the accuracy of the matrix inversion polynomial can be controlled via user input. The results show that success probabilities vary between 10⁻⁶ and 10⁻² for the cases considered. More accurate approximations have lower success probabilities and require longer circuits. Less accurate approximations are analysed and show that variations during the non-linear iterations are related to the eigen content of the right-hand side vector. The use of amplitude amplification is shown to be able to increase success probabilities from 10⁻⁶ to 10⁻², in accordance with theory, but at a cost of a 100 times increase in circuit depth. Whilst these results are specific to the fluid flow test cases, they are generalisable to other types of linear solvers.</p>