diameter never exceeds 3 m are employed very seldom, because they are rather inconvenient for inspection and maintenance.
回填式压力钢管用钢管或钢筋混凝土管制成，放置在卵石或一个回填沟的混凝土垫层上。最常用的钢筋混凝土压力管道直径最大可达6米（有时可更大）。直径不超过3米的钢压力管道应用的非常少，因为它们在检修和维护方面相当不方便。
Open (exposed) penstocks are, in effect, welded steel pipelines up to 9 m in diameter, installed on concrete supports placed directly along the slope. There also exist reinforced concrete and wood constructions, but these are used less frequently. Open penstocks may be either of the continuous (rigid) type or of the split multispan type. Continuous penstocks are rigidly fixed at the two ends by anchorage supports and, therefore, suffer considerable stresses as they expand or contract under temperature variations. This can readily be avoided by splitting the penstock into several spans each of which is fixed by anchorage supports of its own. An expansion joint is installed in each span to allow the penstock to expand or contract under temperature variations without giving rise to any additional stresses. Between the anchorages, the pipes rest on a number of intermediate supports designed to carry the weight of the filled penstock only and to provide for the free movement of the pipe caused by thermal expansion or contraction.
事实上，明管（暴露）压力管道是直径达到9米的焊接钢管道，直接沿着坡安装在混凝土支撑物上。同事存在钢筋混凝土和木质建筑物，但是这些用的很少。明管压力钢管可能是连续（刚性）式或分段式。连续式压力管道被通过镇墩刚性地固定在两端，然后在其受到温度变化导致的扩大或收缩时受到相当大的压力。这可以通过将压力管道分成几段时就可避免，每段由本身的镇墩固定。每段中都安装了伸缩机以允许压力光管在温度变化是扩大或收缩而不增加任何附加应力。在镇墩之间，管道也放置在很多的支墩上，它们被设计于仅承受充满压力钢管的重量，且提供由热膨胀或收缩引起的管道的自由运动。
4. Water Hammer in Penstocks 4. 压力管道中的水击
When the flow of water through, say, a penstock is stopped too rapidly, the water pressure suddenly rises above the normal level and might cause the penstock to burst. Quite appropriately, this phenomenon has come to be known as the water hammer.
当水流通过时，例如，一个压力管道非常迅速地关闭了，水压迅速上升至正常水平以上且可能导致压力管道爆裂。这个现象被很恰当地称作“水击”。
Picture to yourself a conduit of length L and cross-sectional area F through which water uniformly flows at a velocity v(Figure 1). Assume also that a gate installed at the end of the conduit (or wicket gates in the case of a penstock) has closed instantly and brought the water to a sudden stop. Following the stop, the kinetic energy of the water vanishes, resulting in an equivalent increase in its potential energy, which manifests itself in a pressure rise Δph.
设想水流以v的速度均匀通过一条长为L且断面面积为F的输水管（图1）。再假设安装在输水管尾端的闸门（或者在压力管道情况下的导叶闸门）瞬时关闭并导致水流突然停止。随着该停止，水流的动能小时，引起了在其势能上的相等的增加，这在其展现为Δph的压力上升。
Since the conduit walls possess certain elastic properties, the pressure rise cannot propagate instantaneously throughout the conduit. Over a time interval dt, the pressure riseΔph will travel a distance dl. Within dl, the walls will expand and the conduit will “swell” as shown schematically in Figure 1(a). As this process goes on, the pressure wave travels up the conduit to the forebay at a velocity a. The velocity of the pressure wave depends on the elastic characteristics of the conduit and water and would be equal to the velocity of sound in water (1425ms-1) if the conduit walls were absolutely rigid. Under real conditions, however, it is determined as
??=
1425 1+??0
??????
（1）
where ??0 is the modulus of elasticity of water (2×103MPa)，E is the modulus of elasticity of the wall material (2×105MPa for steel), ?? is the wall thickness, and D is the conduit diameter. For steel conduits, a is approximately adopted as 1000 ms-1.
由于输水管壁具有一定的弹性性能，该压力上升不能立刻通过输水管传播。在dt的时间间隔内，压力上升Δph会传播一个dl的距离。如图1所示，在dl内输水管壁将会扩大且输水管将“膨胀”。随着这个过程的推进，该压力波以速度a沿着输水管传播至前池。压力波的速度取决于输水管的弹性特性和水，并且如果输水管壁为绝对刚性，那么它的速度将等于声音在水中的传播速度（1425ms-1）。然而在实际情况中，它被确定为
??=
1425?? 1+??0
????
（1）
其中??0是水的弹性模量（2×103MPa），E是壁材料的弹性模量（钢材2×105MPa），??是壁厚，且D是输水管直径。对于钢输水管，a近似采用1000 ms-1。
Figure 1 Water hammer in a penstock
(a) forward pressure wave; (b) backward pressure wave.
图1 压力管道中的水击
（a）向前压力波；（b）向后压力波。
Following the sudden closure of the gate, Δph reaches its ultimate value Δpul which can be found by equating the change in water momentum over a time dt to the impulse of the associated force
????
Whence
??(d??)??=Δpul
????d????
=ΔpulFdt
Considering that dl/dt=a, we may write for the ultimate pressure rise and the ultimate water-hammer head
????????=(g)??g （2） ??H????=
???? g????
The second line in Eq.（2） is called the Zhukovsky formula.
随着闸门的突然闭合，Δph达到了它的最终值Δpul，这可以通过将水动量在dt时间内的变化与相应力的冲量作等式而获得
????
由此得到
??(d??)??=Δpul
考虑dl/dt=a，我们可以写出最终压力上升和最终水击水头为
????????=()??g （2）
g????
????d????
=ΔpulFdt
??H????=
???? g方程（2）中的第二行被称作茹科夫斯基公式。
Let us now consider what happens as the positive pressure wave resulting from the water hammer travels up the penstock to the forebay. Upon reaching the forebay, it is reflected back from the open end of the penstock as a negative pressure wave which has the same magnitude and travels back at the same velocity a as the positive wave (Figure 1b). As soon as the backward negative wave reaches the closed gate, it is again reflected back to the open end as a positive wave. This process goes on until the waves gradually die out because of the inevitable losses of energy taking place under real conditions. The time of one round trip of the wave is called the time of one interval or the critical time of the pipe. It is expressed in seconds as
tcr=a （3）
现在我们考虑由水击沿着压力管道传播到前池而产生的是正水击波。一旦到达了前池，它就会以负水击波的形式从压力钢管的开放尾端反射回去，它大小相同且以与正波相同的速度回传（图1b）。一旦向后的负波达到关闭的闸门，它又作为正波被反射至开口尾端。这个过程一直持续，直到由于实际情况中发生的不可避免的能量损失使得水波逐渐消失。水波往返一次的时间被称作1间隔的时间或管道的临界时间。它以秒为单位表示为
tcr=a （3）
Under real conditions, the gate is never closed instantly, so the negative pressure wave finds itself superimposed on the positive wave, which to a certain extent relieves the pipe of the water hammer. As a result, Δph is always smaller thanΔpul.
在实际情况中闸门并从不是瞬时关闭，所以负波与正波相叠加，这在某种程度上缓解了管道的水击。作为结果，Δph总是比Δpul小。
2??2??
5. Surge Tanks 5. 调压井
The simplest means of eliminating positive (or negative) water-hammer pressure and improving speed-regulation conditions is to provide a bypass to take the rejected flow. This may be accomplished by what are known as surge tanks. Surge tanks are generally installed either at the lower end of a pressure diversion conduit to link the diversion conduit to the penstocks or at the lower end of long penstocks leading from a dam to an isolated power house. Surge tanks may also be provided at the upper end of a long tailrace diversion system. Whether or not a conduit requires a surge tank depends on its Tw. As a rule, the need for a surge tank arises when
Tw＞3 to 6 （1）
消除正（或负）水击压力和改善转速调节条件的最简单的方式是提供一个旁通道以接纳反射水流。这可以通过所谓的调压井完成。调压井通常安装在压力导流输水管的低端以连接导流管和压力管道，或者在自大坝到一个独立发电厂房的长压力管道的低端。调压井也可放置在一个长的尾水系统的上端。输水管是否需要一个调压井取决于其Tw。一般来说，当下述情况发生时，就需要调压井
Tw＞3 to 6 （1）
Figure 1 principle of operation of surge tank
1—pressure gradient when surge-tank level is a maximum; 2—pressure gradient when surge-tank level is a minimum. 图1 调压井的运行规则
1—当调压井级别最高时的压力梯度； 2—当调压井级别最低时的压力梯度。
图1 调压井运行原则
1-当调压井水位最高时的压力梯度； 2-当调压井水位最低时的压力梯度。
Let us discuss the principle of operation of a surge tank (Figure1). When the turbines
operate at a constant velocity and a uniform discharge, the free-surface level of the tank is by ????????=+
????22??
lower than the static headwater level, where ???????? is the head lost in the diversion
system. When the wicket gates are closed and the turbine is unloaded, the flow through the penstocks comes to a standstill, and the water arriving with the initial velocity is rejected into the surge tank, thereby raising its level. As this takes place, the kinetic energy of the flowing water is converted into the potential energy of the water stored above the normal surge-tank level.
我们来讨论调压井的运行规则（图1）。当水轮机以一个恒定速度和均匀流量时运行，井的自由表面水位比（水库）静止上游水位低????????=+
????22??
，其中????????是输水系统的水头损
失。当水轮机甩负荷导叶关闭时，压力管道中的水流突然停止，而引水道中仍以初始流速流来的水体被迫流入调压井，从而使调压井中的水位升高。当这种情况发生时，水流的动能转换为势能储存在调压井正常水位之上的水体中。
The pressure wave which is reflected from the free surface cannot propagate into the conduit and is eventually suppressed, resulting in an appreciable decrease inζ. When all of the kinetic energy of the rejected water is converted into potential energy, the tank level becomes by Zm higher than the head water level. At this instant, the velocity of stream flow through the diversion conduit equals zero. However, this state is by no means stable, and the water soon begins to flow out of the tank into the conduit.
从自由表面反射的压力波不能传递至输水管并最终被抑制，导致了ζ中明显的减少。当反射水流的所有动能都转换成势能时，调压井水位比上游水位高出Zm。此时，流过输水系统的水流速度等于零。然而，这个状态并不是稳定的，水流很快就开始回流入输水管。
The accompanying pressure fluctuations are eventually damped by the friction between the water and the walls of the conduit and the surge tank. After the fluctuations have been suppressed completely, the water in the tank attains a new level corresponding to the new load on the turbine or equal to the static headwater level if the gates have been closed to zero. Assuming the cross-sectional area of the tank as ????, the cross-sectional area of the diversion conduit as ????????, and the length of the conduit as L, the period of pressure fluctuations may be developed as
??=2?? ?????? （2）
??????
????
伴随的压力波动最终通过水和输水管壁及调压井之间的摩擦而减弱。在波动被完全抑制后，井中的水达到了与水轮机上新负荷相对应的水位，或者如果闸门完全关闭时与静止上游水位相同。假设井的断面面积是????，输水管的断面面积是????????，且输水管的长度是L，那么压力波动的时间就可以表示为
??=2??
????????????????
（2）
When the load on the turbines is suddenly increased, the tank level falls by, and similar pressure fluctuations take place. The analysis of this situation should be based on the lowest headwater level. The thing is that the pressure gradient following the drop in tank level will give the elevation above which the diversion conduit ought not to be laid if it is to be protected against vacuum.
当水轮机的荷载突然增加时，井中水位随之下降，且发生相似的压力波动。对这种情况的分析应该基于最低的上游水位。问题是，如果要防止出现真空，就要保证随着井水位下