Wikipedia states that mass flow rate is a scalar quantity, however

Mass Flow Rate= Density x Cross Sectional Area x Velocity

and velocity is a vector quantity, so this would imply Mass Flow Rate is a vector?

What is wrong here?

  • $\begingroup$ hi hint: so check the dimensions (units used) on each side on the equation, if you get scaler quantity on one side then.... remember the dot product rule and apply a unit normal vector to the area regards $\endgroup$ – user74893 Mar 28 '15 at 12:31
  • $\begingroup$ The units alone can not tell you about the scalar or vector nature of something. Have a look at how you would calculate how much of a quantity flows through an area and you will get your answer. $\endgroup$ – Chris2807 Mar 28 '15 at 12:37

You are missing the bit under-braced here: $$ \dot{m}=\rho\underbrace{\mathbf A\cdot\mathbf v} $$ This is a dot product, which takes two vectors and returns a scalar: $$ c=\mathbf a\cdot\mathbf b=a_xb_y+a_yb_y+a_zb_z $$ So the mass flow rate is indeed a scalar value.

| cite | improve this answer | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.