(Solved):   The velocity potential for a certain inviscid, incompressible flow field is given by the e ...

 

The velocity potential for a certain inviscid, incompressible flow field is given by the equation \[ \varphi=10 x^{2} y-\left(\frac{10}{3}\right) y^{3} \] where \( \varphi \) has the units of \( \mathrm{m}^{2} / \mathrm{s} \) when \( x \) and \( y \) are in meters. Determine the pressure at the point \( x=1.8 \mathrm{~m}, y=1.8 \mathrm{~m} \) if the pressure at \( x=1 \mathrm{~m}, y \) \( =1 \mathrm{~m} \) is \( 2600 \mathrm{kPa} \). Elevation changes can be neglected, and the fluid is water. \[ p_{2}= \] \( \mathrm{kPa} \)