Fluid friction from sudden expansion

Example 5-6 Friction Loss in a Sudden Expansion. Figure 5-7 shows the flow in a sudden expansion from a small conduit to a larger one. We assume that the conditions upstream of the expansion (point 1) are known, as well as the areas A and A2. We desire to find the velocity and pressure downstream of the expansion (V2 and P2) and the loss coefficient, Kt. As before, V2 is determined from the mass balance (continuity equation) applied to the system (the fluid in the shaded area). Assuming constant density,... 

Friction loss from sodden expansion of cross section. If the cross section of the conduit is suddenly enlarged, the fluid stream separates from the wall and issues as a jet into the enlarged section. The jet then expands to fill the entire cross section of the larger conduit. The space between the expanding jet and the conduit wall is filled with fluid in vortex motion characteristic of boundary-layer separation, and considerable friction is generated within this space. This effect is shown in Fig. 5.13. 

The friction loss from a sudden expansion of cross section is proportional to the velocity head of the fluid in the small conduit and can be written... 

Friction loss from sudden contraction of cross section. When the cross section of the conduit is suddenly reduced, the fluid stream cannot follow around the sharp corner and the stream breaks contact with the wall of the conduit. A jet is formed, which flows into the stagnant fluid in the smaller section. The jet first contracts and then expands to fill the smaller cross section, and downstream from the point of contraction the normal velocity distribution eventually is reestablished. The cross section of minimum area at which the jet changes from a contraction to an expansion is called the vena contracta. The flow pattern of a sndden contraction is shown in Fig. 5.14. Section CC is drawn at the vena contracta. Vortices appear as shown in the figure. 

Example 9.2. We wish to pump 200 gal/min of water at 150°F from a sump. We have a PD pump which can reduce the absolute pressure in its cylinder to 1 psia. We have an 3 g (for the pipe only) of 4 ft. The friction effect in the inlet valve may be considered the same as that of a sudden expansion (see Sec. 5.5) with the inlet velocity equal to the fluid flow velocity through the valve, which here is lOft/s. The atmospheric pressure at this location is never less than 14.5 psia. What is the maximum elevation above the water level in the sump at which we can place the pump inlet ... 

EXAMPLE 2.8-4. Friction Loss in a Sudden Enlargement A mechanical-energy loss occurs when a fluid flows from a small pipe to a large pipe through an abrupt expansion, as shown in Fig. 2.8-4. Use the momentum balance and mechanical-energy balance to obtain an expression for the loss for a liquid. (Hint Assume thatPq = p, and Vq = Vj. Make a mechanical-energy balance between points 0 and 2 and a momentum balance between points 1 and 2. It will be assumed that pi and P2 are uniform over the cross-sectional area.)... 

Losses in sudden expansion. For the frictional loss for a non-Newtonian fluid in laminar flow through a sudden expansion from to D2 diameter, Skelland (S2) gives... 

Pressure drop on the tube-side of a shell and tube exchanger is made up of the friction loss in the tubes and losses due to sudden contractions and expansions and flow reversals experienced by the tube-side fluid. The friction loss may be estimated by the methods outlined in Section 3.4.3 from which the basic equation for isothermal flow is given by equation 3.18 which can be written as ... 

---