Fluid Flow, Continuity, and Bernoulli’s Equation (4B) Practice Test

A research group studies an incompressible fluid flowing through a horizontal constriction. They report that in the constricted region the speed increases by a factor of 4 relative to upstream ($v_2 = 4v_1$). Ignoring viscosity, which relationship between the dynamic pressure terms is most consistent with Bernoulli’s equation?

A saline solution (density $\rho = 1000\ \text{kg/m}^3$) flows steadily through a horizontal catheter that narrows from cross-sectional area $A_1 = 4.0\ \text{mm}^2$ to $A_2 = 1.0\ \text{mm}^2$. The average speed in the wide section is measured as $v_1 = 0.50\ \text{m/s}$. Assuming incompressible flow and no leakage, what would be expected for the average speed $v_2$ in the narrow section?