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We investigate the transverse momentum dependence of pion HBT radii on the basis of a hydrodynamical model. Recent experimental data show that $R_{\text{out}}/R_{\text{side}} < 1$, which suggests a strong opaqueness of the source. In addition to the opaqueness naturally caused by transverse flow, we introduce an extrinsic opacity by imposing restrictions on the pion emission angle. Comparing the HBT radii obtained from the normal Cooper-Frye prescription and the opaque emission prescription, we find that $R_{\text{out}}/R_{\text{side}}$ is less than unity only for small values of the transverse momentum with an opaque source. However, HBT radii for large values of the transverse momentum are dominated by the transverse flow effect and are affected less by the source opaqueness.