Question

The indicator dilution method is a technique used to determine flow rates of fluids in channels for which devices like rotameters and orifice meters cannot be used. A stream of an easily measured substance (the tracer) is injected into the channel at a known rate and the tracer concentration is measured at a point far enough downstream of the injection point for the tracer to be completely mixed with the flowing fluid. The larger the flow rate of the fluid, the lower the tracer concentration at the measurement point.

A gas stream that contains 1.50 mole% CO2 flows through a pipeline. 20.0 kg/min of CO₂ is injected into the line. A sample of the gas is drawn from a point in the line 10 meters downstream of the injection point and found to contain 2.3 mole% CO₂.
Eighteen seconds elapses from the instant the additional CO₂ is first injected to the time the CO₂ concentration at the measurement point begins to rise. Assuming that the tracer travels at the average velocity of the gas in the pipeline (i.e. neglecting diffusion of CO2), estimate the average velocity (m/s). If the molar gas density is 0.123 kmol/m3, what is the pipe diameter?

Answer 1

To calculate the new flow rate for different changes, consider the factors affecting flow rate such as pressure difference, viscosity, tube length, and tube radius. The flow rate is determined by the formula Q = A * v, where A is the cross-sectional area and v is the velocity of the fluid. The new flow rate can be calculated based on the changes in these factors.

Step-by-step explanation:

To calculate the new flow rate for different changes, we need to consider the factors affecting flow rate. The formula for flow rate is Q = A * v, where Q is the flow rate, A is the cross-sectional area, and v is the velocity of the fluid.

(a) If the pressure difference increases by a factor of 1.50, the flow rate also increases by the same factor.

(b) If a new fluid with 3.00 times greater viscosity is substituted, the flow rate decreases by the inverse of the viscosity factor, which is 1/3.00.

(c) If the tube is replaced by one having 4.00 times the length, the flow rate remains the same as the original since the cross-sectional area is not changing.

(d) If another tube is used with a radius 0.100 times the original, the flow rate decreases by the factor of 0.100 squared, which is 0.010.

(e) If yet another tube is substituted with a radius 0.100 times the original and half the length, and the pressure difference is increased by a factor of 1.50, the flow rate decreases by the factor of 0.100 squared and increases by the factor of 1.50, which is 0.015.