Water flows through a long horizontal tube. Suppose P_A and P_B represent the pressures at two distinct points A and B within the tube.

Step-by-step solution

For an ideal incompressible fluid flowing through a horizontal tube, Bernoulli's equation states that: P + 1 2 v^2 = constant Applying this principle at points A and B within the tube: P_A + 1 2 v_A^2 = P_B + 1 2 v_B^2 For the pressures at both points to be equal ( P_A = P_B ), the velocities of the fluid at these points must also be equal ( v_A = v_B ). According to the equation of continuity for an incompressible fluid: A_A v_A = A_B v_B Substituting v_A = v_B into the continuity equation gives: A_A = A_B Therefo