Suppose the vertical pipe of Prob. 10–112 is now horizontal instead. In order to achieve the same volume flow rate as that of Prob. 10–112, we must supply a forced pressure gradient. Calculate the required pressure drop between two axial locations in the pipe that are the same distance apart as z₂ and z₁ of Fig. P10–112. How does modified pressure P´ change between the vertical and horizontal cases?

Data from Problem 112

Water falls down a vertical pipe by gravity alone. The flow between vertical locations z₁ and z₂ is fully developed, and velocity profiles at these two locations are sketched in Fig. P10–112. Since there is no forced pressure gradient, pressure P is constant everywhere in the flow (P = P_atm). Calculate the modified pressure at locations z₁ and z₂. Sketch profiles of modified pressure at locations z₁ and z₂. Discuss.

FIGURE P10–112

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