Question

An orifice meter is to be calibrated for the measurement of the flow rate of a stream of liquid acetone. The differential manomter fluid has a specific gravity of 1.10. The calibration is accomplished by connecting the orifice meter in series with a rotameter that has been previously calibrated for acetone, adjusting a valve to set the flow rate, and recording the flow rate ( determined from the rotameter reading and rotameter calibration curve) and the differential manometer reading, h. The preocdeure is repeated for several valve settings to generate an orifice meter calibraiton curve of flow rate versus h. The following data are taken. Manometer Reading h(mm)- 0, 5, 10, 15, 20, 25, 30. Their respective Flow rates V(mL/s)- 0, 62, 87, 107, 123, 138, 151.

a) For each of the given readings, calculate the pressure drop across the orifice, delta P(mm Hg).

Answer 1

The pressure drop across the orifice is calculated using the manometer readings, the specific gravity of the manometer fluid, and the known density of mercury, factoring in the conversion between mm and cm and the constant of gravitational acceleration.

Step-by-step explanation:

To calculate the pressure drop across the orifice (ΔP) for each manometer reading in mm Hg, we use the fact that pressure is proportional to the height of the manometer fluid column (h), the density of the fluid (ρ), and the acceleration due to gravity (g).

Since the manometer fluid has a specific gravity (SG) of 1.10, its density is 1.10 times that of water, and for mercury, we use its density as a reference (ρ_Hg = 13.6 g/cm³). Given that 1 cm³ = 1 mL, the pressure drop can be calculated as ΔP = h ρ_mano g / ρ_Hg, where ρ_mano is the density of the manometer fluid. The gravitational acceleration (g) is approximately 9.81 m/s², and ρ_mano can be found by multiplying the SG of the manometer fluid by the density of water (1.00 g/cm³). Converting mm to cm and simplifying, the pressure drop for each reading can be computed.