Effective closing time factor
Reduced free flow area in the throttle control system:
fr - reduced free flow area in the throttle control system - []
Q - flow coefficient - []
Qmax - max. flow coefficient - []
Relative Flow:
Qp - relative Flow - []
fr - reduced free flow area in the throttle control system - []
p - pressure parameter - []
Pressure parameter:
p - pressure parameter - []
Δh - theoretical pressure in the closure at full opening - [m]
h0 - rated net head - [m]
Theoretical pressure in the closure at full opening:
Δh - theoretical pressure in the closure at full opening - [m]
v0 - valve speed - [m/s]
g - gravitational acceleration - [m/s2]
ξ - local loss factor for open valve - []
Valve speed:
v0 - valve speed - [m/s]
Q0 - flow - [m3/s]
D0 - valve diameter - [mm]
Effective closing time factor:
cef - effective closing time factor - []
Qpn - relative flow in position n - []
Flow characteristics:
The flow characteristic is the dependence of the actual flow rate on the position of the control actuator of the control system.
The flow characteristics of Fig.1-7 are the dependence of the actual flow rate on the position of the valve of the control system.
Note: The flow characteristics (depending on the valve manufacturer) that are dependent on the position of the valve must be recalculated for dependence on the position of the actuator. Because before the actuator may be a member (crank mechanism, ...) that is not linear.







Example:
We have to determine the difference between the effective shut-off time for the flow characteristic of the valve and the flow characteristic of the control actuator (hydraulic cylinder) according to Fig.8 shut-off butterfly valve DN300 with the following parameters:
h0 = 33m; Q0 = 0,314 m3/s; ξ = 0,106
0 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | |
Q1 | 0,951 | 0,885 | 0,733 | 0,531 | 0,373 | 0,249 | 0,183 | 0,123 | 0,073 | 0,035 | 0,000 |
Q2 | 0,951 | 0,888 | 0,755 | 0,583 | 0,433 | 0,306 | 0,218 | 0,155 | 0,102 | 0,047 | 0,000 |

Q1 - flow characteristic of the valve
Q2 - flow characteristic of the control actuator
Valve speed:
Theoretical pressure in the closure at full opening:
Pressure parameter:
0 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | |
Qp1 | 1,000 | 0,997 | 0,989 | 0,964 | 0,918 | 0,827 | 0,729 | 0,577 | 0,385 | 0,196 | 0,000 |
Qp2 | 1,000 | 0,998 | 0,990 | 0,973 | 0,941 | 0,879 | 0,787 | 0,667 | 0,505 | 0,259 | 0,000 |

Qp1 - relative flow characteristic of the valve
Qp2 - relative flow characteristic of the control actuator
cef1 - effective closing time factor (valve) - []
cef2 - effective closing time factor (control actuator) - []
Literature:
F. Strohmer: Investigating the characteristics of shutoff valves by model tests. Water Power & Dam Construction 1977
By G. L. Beichley, M. ASCE and A. J. Peterka, F. ASCE: Hydraulic design of Hollow-Jet valve stilling basins. Journal of the hydraulics division 1961
Stanislav Kratochvil: Vodní nádrže a přehrady. 1961
Б. И. ЯНЬШИН: ЗАТВОРЫ И ПЕРЕХОДЫ ТРУБОПРОВОДОВ. 1962
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