Pressure drop at pipe outlet

If there were no losses present, one would expect that the velocity would decrease as the flow entered the larger vessel/pipe, with the reduction in kinetic energy leading to a pressure increase. But the situation is changed by the frictional losses caused by turbulence eddies at the vessel inlet. The extent of any increase in pressure may be investigated using 

Integrating this between stations 3 and 4 . where the specific volume remains constant at v but the pipe cross-sectional area changes, we achieve  

For the important case of discharge into a large vessel, the velocity C4 = 0, and so (4.56) becomes 

Allowing for a non-zero value of F3-4, equation (4.55) may be rearranged to give  

To evaluate the term, p v — p4v, we apply the principle of the conservation of linear momentum to the section of flow between stations 3 and 4 . The net force in the direction of flow is equal to the rate of momentum leaving minus the rate of momentum entering the section. Assuming pressure equalization at p3 along the whole flow front at station 3, we may write  

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