Example calculation of liquid flow

The pipe is standard commercial pipe of diameter of 250 mm and length 60 m. It has a smoothly tapering entrance, two right-angled bends as shown, and rises 16 m just before the valve. The discharge vessel is 10 m after the valve, and is positioned 4 m above it. The valve is a 6-inch conventional-disc butterfly, with full-open coefficients CJ. = 1750 US gall min psi , Km = 0.3, Kc = 0.25. The supply vessel contains water at 10 bar and 120°C, while the discharge vessel has a pressure of 4 bar. 

It is known that the design flow is I65kg/s. However, in this transient, the valve is initially 27° open, but after 10 seconds the valve is ramped over a period of half a minute to 54° open. Calculate the flow through the valve as a function of time, and estimate whether it becomes choked and whether cavitation occurs. 

Velocity head drop across the 50 m of pipe before the valve follows from equation (4.46) as 

The fact that the entrance is smoothly tapered allows us to put Kcon 0 (see Chapter 4, Section 4.10), but we need to add the velocity-head drop from the two right-angle bends, ATj, = 0.75 from Table 4.1, to produce the total velocity-head drop, K, between the upstream vessel and the valve Kut = + 2 x 0.75 = 5.1. 

Calculate line conductance upstream of valve using the velocity-head to conductance equation (4.52)  

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