An ideal, incompressible fluid of density \(\rho\) flows through a horizontal pipe. At section 1, the pipe has a cross-sectional area \(A\) and the fluid speed is \(v\). The pipe then narrows to section 2, which has a cross-sectional area \(\frac{1}{3}A\). Which of the following is a correct expression for the pressure difference \(P_1 - P_2\) between section 1 and section 2?