x ray streak camera is an important equipment for time resolved measurement in the field of inertial confinement fusion. Its dynamic range indicates the ability that effectively measuring the intensity of incidence x ray. The photoelectron pulse will be broaden in passing through the photocathode-to-mesh region because of space charge effect. This limits the dynamic range of the streak camera. This paper adopts a fluid model, making use of particle conservation, momentum conservation, and Poisson equations to deduce the widening of the electron pulse and derive the change in the electron density distribution. The results can be used to evaluate the dynamic range of the streak camera.