When a liquid is subjected to very high pressures, its density may increase measurably. A laboratory investigates this effect for a sample of mineral oil. The researchers load the oil into a rigid steel cylinder whose volume is constant at 1.50L. By adding small steel weights to a piston, they steadily increase the gauge pressure on the oil and record the total mass inside the cylinder at each pressure setting.
Part of their data set is shown below.
Gauge Pressure (MPa)
Total Mass of Oil (kg)
0.10
1.283
25.0
1.294
50.0
1.304
75.0
1.312
100.0
1.319
(Note: The cylinder is sealed; the only change is in the mass of oil forced into it by the piston.)
Use the information and data provided to analyze the assumption that the oil behaves as an incompressible fluid.
(a) For each pressure listed, calculate the density of the oil in the cylinder.
(b) Describe qualitatively the trend you observe in density versus pressure and state whether the data support or refute the incompressibility assumption.
(c) Suppose a mechanical engineer uses the oil at a gauge pressure of 75 MPa in a hydraulic system but models it as incompressible with the density you found at 0.10 MPa. Estimate the percent error this assumption introduces into any mass-flow-rate calculation.
(d) Explain how the presence of viscosity, if it were also ignored, could compound or mitigate the error discussed in part (c).