Pressure Force in a fluid The solution defined in Pressure over a surface gives the basic definition of pressure on a surface.
In an incompressible, inviscid, steady flow, plane flow, the Force on any object may be due to pressure force and it is defined as shown.
$F_p = \dfrac{\rho}{2}\int_A V^2 d\vec{A} = \dfrac{\rho}{2}\int_A V^2 \hat{e_n} dA $
, where $\hat{e_n} $ is the normal vector of the elemental surface $dA$.
$ \vec{V}$ is the mean velocity of flow, $\rho $- the density
From where do we get the above expression for pressure force. 
The definition of normal force in  fluid is given by 
$\sigma_{ii} = 2 \mu \dot{\epsilon_{ii}}  + (p - \dfrac{2}{3} \nabla . \vec{V})$(general case).  I think the pressure, $p$ is defined along with the normal stress components.
$\sigma_{ii}$ - the normal stress components
$\dot{\epsilon_{ii}}$ - the normal strain rates.
 A: Since you are dealing with incompressible, inviscid flow, the effects of viscosity are absent and the incompressibility condition $\nabla \cdot \mathbb{v} = 0$ applies.  Even in a moving fluid, the stress tensor is isotropic under these conditions with $\sigma_{ij} = - p \delta_{ij}$ where $\delta_{ii} = 1 $ and $\delta_{ij} = 0$ if $i \neq j.$  When the fluid is at rest, the static pressure $p$ is just the thermodynamic pressure.  When the fluid is moving, $p$ represents the average normal force acting on a fluid element.
The Euler equation for steady flow, expressing conservation of momentum, relates the fluid velocity to the pressure
$$\rho\mathbb{v} \cdot \nabla \mathbb{v} = -\nabla p.$$
Here I have ignored body forces which usually (eg., gravity) can be absorbed into the pressure.  From here we can derive the Bernoulli equation
$$p + \frac{\rho}{2}|\mathbb{v}|^2 = C$$
where $C$ is constant along a streamline (or constant everywhere in irrotational flow).  The surface of an object must coincide with a streamline since the fluid velocity normal to the surface is zero. In any case, the constant has no impact when integrated over a closed surface:
$$\int_A C\mathbb{n} \, dA = 0$$
This follows from the divergence theorem.  If $A$ encloses the region $V$, then for any constant vector $\mathbb{b}$ we have 
$$\mathbb{b} \cdot \int_A \mathbb{n} \, dA = \int_A \mathbb{b} \cdot \mathbb{n} \, dA = \int_V \nabla \cdot \mathbb{b} \, dV = 0,$$
which implies
$$\int_A \mathbb{n} \, dA = 0.$$
Thus, 
$$F_p = -\int_A p \mathbb{e}_n \, dA = \frac{\rho}{2}\int_A |\mathbb{v}|^2\mathbb{e}_n \, dA $$
