Abstract: The time-domain analytical formulation for acoustic velocity prediction in a uniform mean flow is considered theoretically and numerically. For acoustic velocity prediction based on the permeable surface principle, a theoretical analysis of the source terms on the right hand of the convective vector wave equation shows that part of the permeable surface source contributing to the acoustic velocity propagation is neglected. Based on the time-domain integral formulation V1A-M for the convective vector wave equation, an analytical formulation CV1A-M is developed by further considering the contribution from the missing permeable surface source. The acoustic velocity radiations are predicted numerically using formulations V1A-M and CV1A-M for a stationary/rotating monopole and dipole in a uniform mean flow. The numerical solutions of formulation CV1A-M agree well with the theoretical values, while the numerical solutions of formulation V1A-M differ significantly from the theoretical values due to the neglection of part of the loading source on the permeable surface. The radiation from a dipole in a uniform mean flow dose not induce any vortical disturbance and the linearised Euler equation can be used to describe the relationship between acoustic velocity and acoustic pressure.