Doppler ultrasound in orifice flow. In vitro studies of the relationship between pressure difference and fluid velocity.

The validity of an orifice equation (Torricelli's law) which expresses a simple relationship between the pressure difference across an orifice and the maximum fluid velocity in the orifice was tested in vitro. An aqueous suspension of barium sulfate particles with a polymer added to attain variations in viscosity, was forced through orifices which ranged in diameter from 0.4 to 4.7 mm. The pressure difference across the orifice was determined with a transducer and the maximum fluid velocity in the orifice was determined with Doppler ultrasound. Tests were performed at Reynolds numbers, fluid viscosities, and pressure differences that spanned the following ranges: 400-25,000, 1-5 cP, and 3-100 mmHg, respectively. At pressure differences larger than 3 mmHg and fluid viscosity 3 cP (approximate viscosity of in vivo blood), Torricelli's law was demonstrated to be valid for orifice diameters larger than 1.6 mm. The validity of the law was found to be relatively insensitive to variations in orifice length.