The pressure structure function ${D}_{P}(r)$ and pressure-gradient correlation ${A}_{\mathrm{ij}}(r\ensuremath{\rightarrow})$ are related to components of the fourth-order velocity structure function ${D}_{\mathrm{ijkl}}(r\ensuremath{\rightarrow})$ on the basis of the Navier-Stokes equation, incompressibility, local homogeneity, and local isotropy. Data from a wind tunnel, as well as numerical simulation, are used to calculate ${D}_{P}(r)$ and thereby show that greater Reynolds numbers are needed to observe an inertial range in ${D}_{P}(r)$ than in ${D}_{\mathrm{ijkl}}(r\ensuremath{\rightarrow}).$ A previous additional supposition relates ${D}_{P}(r)$ and ${A}_{\mathrm{ij}}(r\ensuremath{\rightarrow})$ to the single component ${D}_{1111}(r).$ This additional supposition is shown to be inaccurate for calculation of ${D}_{P}(r)$ and ${A}_{\mathrm{ij}}(r\ensuremath{\rightarrow}).$