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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?

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  • $\begingroup$ 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
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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.

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