284 FLOW RESISTANCE: A DESIGN GUIDE FOR ENGINEERS

Figure 9-1 Flow pattern in throttling and control devices: (a) gate valve, (b) butterfly valve, (c) disk valve, and
(d) globe valve.

4 . The resistance coefficient of open gate valves of different dimensions and designs
differs in magnitude. This difference is mainly due to the relative dimensions of the valve
disk cavity or recess. The smaller the diameter of the gate opening, the larger are the
relative dimensions of the recess. Therefore, the resistance coefficients of open gate valves
of the same type of design are smaller for large disk or gate diameters.
5. When the valve disk is installed on one side of the gate opening, this heavily distorts
the symmetry of the flow. As a result, pressure fluctuations and vibrations of the pipeline
increase substantially. From this point of view, a rectangular gate with valve disks on two
sides moving simultaneously is a Jvantageous [33, 341.
6. In order to reduce the size of the gate valve, as well as the magnitude of forces and
torques required to control it, the flow section in the valve casing is usually contracted. The
contraction is usually symmetrical, but for a one-side motion of liquid it can also be
asymmetric [12]. The contraction of the passage increases the resistance coefficient of the
gate valve.
7. Gate valves and various plugs (conical, spherical, segmented, rollerlike) used in
water supply systems, pressure delivery pipes of hydroelectric stations, and gas and petro-
leum pipelines and other structures and plants can operate both within the system and at its
exit. In the first case they are installed in the straight pipe, in converging-diverging transi-
tion units, or in a converging transition unit (see respective schemes on Diagrams 9-1, 3, 7,
r
and 11 through 17). The values of given in these diagrams do not allow for the additional
losses of velocity pressure at the exit and, correspondingly, the losses in transition pieces
[33, 341.
The total resistance coefficient of the terminal (end) gate valves and plugs, and simi-
larly for gate valves and plugs installed in transition pieces, is determined as &
r
and, correspondingly, 3;,, = + &, where the r s are the values of these coefficients for
!: 1, - +
the terminal gate valves and plugs given on diagrams of Chapter 9 and is determined as r,,
of the converging-diverging and other transition pieces in Diagrams 5-24 and 5-25.
8. In a labyrinth seal, in which baffles are interstitially located on one side and on one
 FLOW THROUGH PIPE FITTINGS AND LABYRINTH SEALS 285

level, the flow passes uniformly. Entering the first gap (Fig. 9-2a), the flow contracts in the
same way as in the case of entrance into a straight channel mounted flush with the wall, or
as in the case of passage through an orifice in a thin wall. When the flow enters the
labyrinth chamber it expands and, due to turbulent agitation, additional fluid is entrained at
the expense of the surrounding medium. When the relative dimensions of the chamber are
sufficiently large (as compared with the gap), a core of constant mass separates from the jet
at the chamber end and, contracting, enters the second gap. The entrained masses of the
surrounding medium separate from the core at the chamber end and move with a circulatory
motion in the chamber until they become once more mixed with the flow. Since the
constant-mass core has a high kinetic energy before it enters the second gap, it will contract
less than in the first gap.
9. The resistance of the labyrinth cell (Fig. 9-2a) is due to the frictional losses in the
gap and the energy losses in the constant-mass core. The latter are made up of two parts:
the difference between the energy stored in the constant-mass core at the beginning and at
the end of the cell, and the losses at the entrance into the next gap.
If the dimensions of the chamber are relatively small, so that

then the jet issuing from the gap into the chamber will fill the entire section. The resistance
in this case is made up of the frictional losses in the gap, the losses at a sudden expansion,
and the losses at entering the next gap, where 6; is the half-width of the labyrinth gap with
recesses on both sides, or the width of the jet in the labyrinth with a recess on one side; 6, is
the half-width of the free jet at the end of the chamber (or, correspondingly, the width of the
jet), in meters; and h,, is the height of the chamber of the labyrinth cell.
According to Abramovich [2]

where S is the length of a free jet (the length of the chamber of a labyrinth cell), m, and a,,,
is the coefficient of the structure (turbulence) of flow, taken, in this case, to be equal to 0.1.
10. In labyrinth seals with protuberances or with a staggered arrangement of baffles
and with large chamber dimensions between the baffles, the jet, being compressed in the
gap, moves toward the protuberances of the labyrinth (Fig. 9-2b). Here, it deflects through
90" and moves directly to the lower wall of the chamber. It then circulates in the chamber

Figure 9-2 Flow pattern in labyrinths: (a) cell of a simple labyrinth and (b)labyrinth with complex flow passage.
286 FLOW RESISTANCE: A DESIGN GUIDE FOR ENGINEERS

and moves along the second chamber toward the second gap. The jet, flowing in the
labyrinth chamber, entrains stationary masses from the surrounding space, causing them to
move with eddy zones forming as a result. Protrusions between the baffles of the labyrinth
lengthen the path of the free jet, which contributes to its attenuation. Labyrinths with
tortuous flow paths are more efficient, since their jet path length, and correspondingly their
resistance, is markedly larger than in labyrinths with straight flow passage.
11. While the valves and throttling devices are of typical Russian designs, there exists
sufficient similarity to US-type devices to allow approximation of pressure losses with
reasonable accuracy provided geometric and flow regime similarity exists.
9-2 DIAGRAMS OF THE RESISTANCE COEFFICIENTS
Various globe and gate valves; Re = w,Dh/v > lo4 Diagram
[25,32,35] 9-1

"Rey"-type globe valve

Forged globe valve

Wedge-type gate valve Steam gate valve with lever gate

Conduit-type gate valve

With two successively installed globe valves (gate valves) the total resistance coefficient is

where for 5, , see 5 of the first stopping device; for S,, see 5 of the second stopping device; P = 4.2 X lo-'
(I/Do = 5 X 10- I/DO;I is the distance between two stopping devices.