Calculate the mass flux when water flows through a pipe of varying diameter

What is the mass flux when water flows through a pipe of varying diameter?

Given data: Water is flowing in a 2.5-in.-diameter pipe at 54ft/sec. If the pipe enlarges to a diameter of 5in, calculate the mass flux.

Answer:

To find the mass flux, the constant mass flow rate is divided by the cross-sectional area of the pipe.

Explanation:

When water flows through a pipe of varying diameter, the mass flow rate should remain constant according to the principle of conservation of mass. This means that the mass flow rate in the smaller pipe section (2.5 in. diameter) is equal to the mass flow rate in the larger section (5 in. diameter).

The equation for mass flow rate is: mass flow rate = density × velocity × cross-sectional area. Since water is incompressible, its density remains constant throughout the flow.

To calculate the mass flux, you divide the mass flow rate by the cross-sectional area of the pipe. The velocity of the water in the larger diameter section can be found using the continuity equation, which relates velocities and cross-sectional areas at two points in the flow. The cross-sectional area of a pipe can be calculated using the formula A = (π/4) × d², where d is the diameter of the pipe.

By applying these formulas and principles, you can accurately determine the mass flux when water flows through a pipe with varying diameter.