Three-dimensional pipe flows with elbows, tees and headers in three different pipe systems are calculated to estimate the effect of asymmetry of axial velocity profile and swirl on measuring accuracy of an orifice flowmeter. It is evaluated how the pressure difference across the orifice is dependent on the upstream straight pipe length and how swirl intensity, swirl angle, and axial velocity distribution affect the measuring error of the orifice flowmeter. From the results, it is found that variation of the pressure difference across the orifice is negligible in case that maximum swirl angle is less than 2$^{circ}$, and also that the pressure difference across the orifice is more sensitive to the asymmetry of axial velocity profile rather than the swirl intensity.