This study explains why observed storms with long concentric eyewall (CE) duration often have a large moat size. A series of slab boundary layer model experiments are conducted with the free atmosphere forcing from different CE structures. The experimental results indicate that the inner eyewall pumping (IEP), the maximum vertical motion at the inner eyewall region, increases with the increase in moat size d and vortex maximum wind vm, the decrease in the inner eyewall radius rm, and increase in inner eyewall vorticity. A scaling law is derived from hundreds of SBL experiments with four variables: IEP win, vortex inner radius rm, vortex maximum wind vm, and moat size d. The dimensionless scaling law is w∗∼d∗, ${w}^{\ast }\sim \sqrt{{d}^{\ast }},$ where w∗ = win/vm, d∗ = ζd/c, ζ is the vorticity 2vm/rm, and c is a constant gravity wave speed. The moat size divided by the Rossby length c/ζ, the dimensionless moat size d∗, combines the effect of the moat size and the vortex pressure gradient force to accelerate the inflow and to enlarge the IEP for inner eyewall convection maintenance. A phase diagram of IEP with vortex structure dimensionless moat ζd/c and vortex intensity vm is constructed based on the scaling law for the aircraft and satellite observations. The eyewall replacement cycle may be viewed as the process to reduce the IEP from the decrease of the vortex intensity and the vortex size of the dimensionless moat. This leads to the ultimate disappearance of the inner eyewall.