Question

current attempt in progress
water is flowing down through the pipe shown in the drawing. point a is at the higher elevation, while b and c are at the same elevation. the cross-sectional areas are the same at a and b. rank the pressures at the three points, largest first.
( p _ { a } , p _ { b } , p _ { c } )
( p _ { b } , p _ { c } , p _ { a } )
( p _ { c } , p _ { b } , p _ { a } )

Explanation:

Step1: Apply the equation of continuity

The equation of continuity is \(A_1v_1 = A_2v_2\). Since \(A_A=A_B\), then \(v_A = v_B\). For the pipe from \(B\) to \(C\), \(A_B < A_C\), so \(v_B>v_C\) (because \(A_Bv_B=A_Cv_C\)).

Step2: Apply Bernoulli's equation

Bernoulli's equation is \(P+
ho gh+\frac{1}{2}
ho v^{2}=\text{constant}\). For points \(A\) and \(B\): \(P_A+
ho gh_A+\frac{1}{2}
ho v_{A}^{2}=P_B+
ho gh_B+\frac{1}{2}
ho v_{B}^{2}\). Since \(v_A = v_B\) and \(h_A>h_B\), then \(P_Aho gh_B+\frac{1}{2}
ho v_{B}^{2}=P_C+
ho gh_C+\frac{1}{2}
ho v_{C}^{2}\). Since \(h_B = h_C\) and \(v_B>v_C\), then \(P_B

Answer:

\(P_C, P_B, P_A\)