Downward Sloping Pipe

When a liquid line slopes downward in the direction of flow, the gain in pressure due to the drop in elevation works counter to the drop in pressure due to friction. A borderline condition exists when the increase in pressure due to the drop in elevation just equals the drop in pressure due to friction.

If the line in Example 9.5 is pitched more steeply than 1 in 173 with the same mass flow rate, the line will run partially filled with liquid. The situation of Fig. 9.5b is the one sought in the draining of a single condenser, Fig. 7.28, where for an ammonia liquid velocity of 0.51 m/s (100 fpm), the same as in Example 9.5, a pitch of 1 in 50 is recommended. Compared to the pitch of 1 in 173 calculated in Example 9.5, enough vapor space will be provided to permit counterflow of the vapor to the liquid. A slope of less than 1 in 173 results in the pipe flowing full.

Example 9.5. What is the downward pitch of an ammonia liquid line carrying 35°C (95°F) liquid at a velocity of 0.51 m/s (100 fpm) in a 50-mm (2-in.) pipe so that the gain in pressure attributable to the liquid head just cancels the pressure drop due to friction?

Solution. The pitch of the pipe, as in Fig. 9.5a, is to be computed so that the gain due to the liquid head cancels the friction pressure drop. Equation 9.1 (9.2), which expresses the pressure drop in Pa (psf), can be revised to compute the loss of head due to friction using either of the relationships:

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