The five diagrams show portions of systems of pipes (with circular cross section

Question

The five diagrams show portions of systems of pipes (with circular cross sections) where a non-viscous incompressible fluid enters at the left and leaves from the right. The diameters of some of the pipes are indicated. The views are either top views of pipe systems in the horizontal plane, or side views of pipe systems in the vertical plane. Find the largest pressure in each diagram and enter your answer from the list of choices below. E.g., if P1 is largest for the first diagram and P2 is largest for the other diagrams, enter ABBBB.

Explanation / Answer

To analyze these diagram we will need following two equations:

Bernauli's equation: P + 1/2**v^2 + *g*h = constant where P is the pressure, is the density of fluid

v is the velocity and h is the reference height.

Continuity Equation: A1*v1 = A2*v2 that is the product of cross-sectoinal area and velocity remains conserved.

(i) Here P1 = P3 ( same height and same cross sectional area meaning same velocity) but P2 is greater as it is located at a lower height.

(ii) Here P2  is greatest as it has highest cross-sectional area and thus lowest velocity.

(iii) Here P1 will be highest (same argument as in (ii) )

(iv) Again P1 will be greatest (same argument as in (ii) and (iii) )

(v) Here P2 is at a lower height (should be more therefore) however P1 has larger area and thus less velocity (should be more therefore). Hence one cannot tell which will be greater unless exact values of parameters are known.

So the correct order is BBAAD

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