An ideal incompressible liquid flows through a pipe with a variable cross-section. At the cross-section with the area A_(1)=8mm^2 , the speed of the liquid equals v_(1)=24mm/s What is the area A_(2) of the second cross-section if the speed of liquid there is v_(2)=6mm/s Please select one answer option A_(2)=18mm^2 A_(2)=2mm^2 A_(2)=32mm^2 A_(2)=1152mm^2

To solve this problem, we can use the principle of conservation of mass, which states that the mass flow rate must be the same at both cross-sections.<br /><br />The mass flow rate is given by the product of the cross-sectional area and the velocity of the liquid. Therefore, we can write:<br /><br />$A_{1}v_{1} = A_{2}v_{2}$<br /><br />Substituting the given values, we have:<br /><br />$8mm^{2} \times 24mm/s = A_{2} \times 6mm/s$<br /><br />Solving for $A_{2}$, we get:<br /><br />$A_{2} = \frac{8mm^{2} \times 24mm/s}{6mm/s} = 32mm^{2}$<br /><br />Therefore, the area of the second cross-section is $A_{2}=32mm^{2}$.<br /><br />The correct answer is: $A_{2}=32mm^{2}$.