Final answer:
The relationship between the flow rate of a gas and its density through a flow meter is linear at low pressures but may deviate at high pressures. The flow rate can be related to mass flow rate via density, and it is directly related to the product of cross-sectional area and velocity for incompressible fluids.
Step-by-step explanation:
The relationship between the flow rate of a gas and its density through a flow meter is generally linear at low pressures. However, this linearity can deviate at higher pressures. The flow rate, which has units of volume per time (like m³/s or L/s), can be converted to mass flow rate using the gas's density. For incompressible fluids, such as water, the density remains constant no matter the flow rate or size of the opening.
Flow rate and velocity are closely related; the relationship can be expressed by the equation Q = A⋅v, where Q is the flow rate, A is the cross-sectional area of the pipe, and v is the velocity of the fluid. This is applicable when dealing with incompressible fluids where the flow rate remains constant at various points in the flow. However, with gases, the relationship can become more complex, involving changes in density at different pressures.