# Is the Mass flow rate (Mass flux) a scalar quantity?

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?

• 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 – user74893 Mar 28 '15 at 12:31
• 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. – 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.