In deriving the continuity equation, we assumed, for simplicity,that the mass fl ow per unit area on the left face wasjust ρ u . In fact, ρ u varies also with y and z , and thus it mustbe different on the four corners of the left face. Account forthese variations, average the four corners, and determinehow this might change the inlet mass fl ow from ρ u dy dz .

Question

In deriving the continuity equation, we assumed, for simplicity,
that the mass fl ow per unit area on the left face was
just ρ u . In fact, ρ u varies also with y and z , and thus it must
be different on the four corners of the left face. Account for
these variations, average the four corners, and determine
how this might change the inlet mass fl ow from ρ u dy dz .

Expert Answer

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Engineering
Mechanical Engineering

Fluid Mechanics

Related Mechanical Engineering Q&A

Find answers to questions asked by students like you.

Q: Q1] A bending moment due to load applied on the head of femur bone which is offset by a distance (x=...

A: Click to see the answer

Q: A horizontal plate is experiencing uniform irradiation on the both upper and lower surfaces. The amb...

A: Given data  Temperature of air Ta= 290K Heat transfer coefficient h = 3030 W/m2K Radiosity of the pl...

Q: Consider the sun, which is considered to be a blackbody with a surface temperature of roughly 5800 K...

A: Given : The surface temperature of sun= 5800 K Assumption : Sun is a black body.  

Q: Considering the right section

A: Click to see the answer

Q: Consider a cubical furnace with a side length of 3 m. The top surface is maintained at 700 K. The ba...

A: Given data:     The side length of the cubical furnance is: L=3 cm The temperature of the top surfac...

Q: Steam enters a horizontal turbine at 350 lbf/in 2 absolute,580 ° C, and 12 ft/s and is discharged at...

A: Given data Steam pressure at inlet of turbine P1 = 350 lbg/in2 Temperature of steam at inlet of turb...

Q: A thermodynamic cycle with 0.1 kg of air has 3 processes as in the figure. Assume air as ideal gas. ...

A: As per the guidelines we will solve the first three subparts of your question.   (a) From the ideal ...

Q: Consider a water-to-water double-pipe heat exchanger whose flow arrangement is not known. The temper...

A: Draw the figure of parallel flow arrangement. From the figure, the heat flows from cold water to h...

Q: Find the current, voltage, and power associated with the 20- . ΚΩ resistor 5 mA 10 k2 0.01V 5 kQ 20 ...

A: Click to see the answer