Question

What is fluid flow velocity?

Answer 1

The flow velocity (v) of any fluid (that may be a gas or a liquid) is defined as a vector field of the fluid, which gives the velocity of any element of the flowing fluid as a function of time (t) and position in space (x). Mathematically, this expression is written as, $v=u(x,t)$. We shall study this equation and its properties in detail in the following section.

Complete step-by-step solution:
The mathematical expression for the fluid flow velocity is stated as:
$\Rightarrow v=u(x,t)$
Now, we can work on this equation to get different types of fluid flow as follows:
Case (1): if the partial differentiation of our above equation with respect to time comes out to be zero, then the fluid is said to be in a steady flow, that is:
$\Rightarrow \dfrac{\partial \left[ u\left( x,t \right) \right]}{\partial t}=0$
Or else, in every other condition it is termed as unsteady flow.
Case (2): If the divergence vector ‘v’ is zero, then the fluid flow is incompressible, that is:
$\Rightarrow \nabla \cdot [u(x,t)]=0$
Or else, in every other condition it is termed as compressible.
Case (3): if the curl of vector ‘v’ is zero, then the liquid flow is irrotational, that is:
$\Rightarrow \nabla \times [u(x,t)]=0$
Or else, in every other condition it is termed as rotational.
If all the three conditions of a liquid are satisfied, then the fluid flow of the liquid is said to be steady.

Note: The fluid flow velocity and the fluid flow rate of a fluid may seem like two similar terms at first, but are completely different from each other. The fluid flow velocity gives us the velocity of a particular element of a fluid section, whereas fluid flow rate is the volume of liquid passing through a certain section in a certain time period.