流動型態轉變時,水流的斷面平均流速稱為臨界流速,把從層流轉變為紊流時的叫上臨界流速,而把紊流轉變為層流時的叫下臨界流速。上臨界流速較大。多次實驗表明,在不同溫度下,管中水流的下臨界流速值比較穩定,上臨界流速易受干擾,其值極不穩定。
原理
![明渠斷面比能與水深關係圖](/img/9/5fd/wZwpmL0MzNzYjN2QDMxcTN1UTM1QDN5MjM5ADMwAjMwUzL0AzLwYzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![臨界流](/img/3/d45/wZwpmL3YDN3AjN3kTN0MTN1UTM1QDN5MjM5ADMwAjMwUzL5UzL3EzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![臨界流](/img/0/f24/wZwpmL3UDO0YTM2kTOwcTN1UTM1QDN5MjM5ADMwAjMwUzL5kzLyEzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
![臨界流](/img/3/3c4/wZwpmLxETM1gjN1ETMxcTN1UTM1QDN5MjM5ADMwAjMwUzLxEzL2QzLt92YucmbvRWdo5Cd0FmLxE2LvoDc0RHa.jpg)
![臨界流](/img/9/e47/wZwpmLxIjM1MDOzIDN0ETN1UTM1QDN5MjM5ADMwAjMwUzLyQzL0MzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
![臨界流](/img/5/b28/wZwpmL2gzN1ETN2IDOwcTN1UTM1QDN5MjM5ADMwAjMwUzLygzLwQzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
臨界流是緩流與急流兩種流態的分界點,臨界流時的斷面平均流速稱為臨界流速,以表示。它與干擾波的波速(c)正好相等,即臨界流是相當於弗勞德數的流動。此時,水流的慣性力作用與重力作用恰好相等。臨界流時的水深稱為臨界水深,以表示。從能量角度來分析,以斷面最低點為基準的斷面單位能量或比能可寫成
![臨界流](/img/4/055/wZwpmL3gzNzYTO1cjN1IDN0UTMyITNykTO0EDMwAjMwUzL3YzL2YzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![臨界流](/img/e/6e3/wZwpmL3gjNyMjMyMTOwcTN1UTM1QDN5MjM5ADMwAjMwUzLzkzLxIzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
底坡較小(渠底與水平面夾角<6°)時,可簡化為
![臨界流](/img/0/a24/wZwpmL3ITO1UDNxQzM3UzM1UTM1QDN5MjM5ADMwAjMwUzL0MzLyEzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![臨界流](/img/8/c90/wZwpmLwcTN5ETO0ETOwcTN1UTM1QDN5MjM5ADMwAjMwUzLxkzLwczLt92YucmbvRWdo5Cd0FmL0E2LvoDc0RHa.jpg)
![臨界流](/img/3/d45/wZwpmL3YDN3AjN3kTN0MTN1UTM1QDN5MjM5ADMwAjMwUzL5UzL3EzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![臨界流](/img/0/f24/wZwpmL3UDO0YTM2kTOwcTN1UTM1QDN5MjM5ADMwAjMwUzL5kzLyEzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
![臨界流](/img/3/3c4/wZwpmLxETM1gjN1ETMxcTN1UTM1QDN5MjM5ADMwAjMwUzLxEzL2QzLt92YucmbvRWdo5Cd0FmLxE2LvoDc0RHa.jpg)
![臨界流](/img/9/e47/wZwpmLxIjM1MDOzIDN0ETN1UTM1QDN5MjM5ADMwAjMwUzLyQzL0MzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
可見,當斷面形狀尺寸和流量大小一定時,渠槽斷面比能()只是水深(h)的函式,且存在一最小值(見圖)。通過對式(1)求一階導數,令其為零,可得臨界流是緩流與急流兩種流態的分界點,臨界流時的斷面平均流速稱為臨界流速,以表示。它與干擾波的波速(c)正好相等,即臨界流是相當於弗勞德數的流動。此時,水流的慣性力作用與重力作用恰好相等。臨界流時的水深稱為臨界水深,以表示。
從能量角度來分析,以斷面最低點為基準的斷面單位能量
![臨界流](/img/4/7c9/wZwpmLzgDN2QDN2kDOwcTN1UTM1QDN5MjM5ADMwAjMwUzL5gzL0YzLt92YucmbvRWdo5Cd0FmLxE2LvoDc0RHa.jpg)
過水斷面上並取a=1.0,上式可寫作
![臨界流](/img/0/a24/wZwpmL3ITO1UDNxQzM3UzM1UTM1QDN5MjM5ADMwAjMwUzL0MzLyEzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![臨界流](/img/3/3c4/wZwpmLxETM1gjN1ETMxcTN1UTM1QDN5MjM5ADMwAjMwUzLxEzL2QzLt92YucmbvRWdo5Cd0FmLxE2LvoDc0RHa.jpg)
![臨界流](/img/9/e47/wZwpmLxIjM1MDOzIDN0ETN1UTM1QDN5MjM5ADMwAjMwUzLyQzL0MzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
![臨界流](/img/3/9c7/wZwpmL3ETM2kjM2MDMxcTN1UTM1QDN5MjM5ADMwAjMwUzLzAzLyUzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![臨界流](/img/3/d45/wZwpmL3YDN3AjN3kTN0MTN1UTM1QDN5MjM5ADMwAjMwUzL5UzL3EzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![臨界流](/img/9/e47/wZwpmLxIjM1MDOzIDN0ETN1UTM1QDN5MjM5ADMwAjMwUzLyQzL0MzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
這就是說,斷面比能()最小時,,為臨界流。臨界水深()即相應於圖中曲線的C點。因此,可用臨界流的水力要素、來區分緩流和急流的流態。
![臨界流](/img/f/b68/wZwpmL0ITN4EzM3UDOwcTN1UTM1QDN5MjM5ADMwAjMwUzL1gzL2MzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![臨界流](/img/c/af0/wZwpmL4QDO4ATMyMTMxcTN1UTM1QDN5MjM5ADMwAjMwUzLzEzL1AzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![臨界流](/img/4/707/wZwpmLxcjM1IDO2UDOwcTN1UTM1QDN5MjM5ADMwAjMwUzL1gzL3MzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
![臨界流](/img/2/04f/wZwpmLyUDM4ADO3ATMxcTN1UTM1QDN5MjM5ADMwAjMwUzLwEzL3gzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
![臨界流](/img/3/9c7/wZwpmL3ETM2kjM2MDMxcTN1UTM1QDN5MjM5ADMwAjMwUzLzAzLyUzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![臨界流](/img/e/f23/wZwpmLyEDMxUDOzUDMxcTN1UTM1QDN5MjM5ADMwAjMwUzL1AzL3UzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
![臨界流](/img/c/a32/wZwpmL3UDM1kDMyMTMxcTN1UTM1QDN5MjM5ADMwAjMwUzLzEzL3UzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
![臨界流](/img/1/c28/wZwpmL0YDMxUDM5ADMxcTN1UTM1QDN5MjM5ADMwAjMwUzLwAzLzAzLt92YucmbvRWdo5Cd0FmLxE2LvoDc0RHa.jpg)
![臨界流](/img/2/a5f/wZwpmLxUTMxEDOyIDOwcTN1UTM1QDN5MjM5ADMwAjMwUzLygzL0UzLt92YucmbvRWdo5Cd0FmL0E2LvoDc0RHa.jpg)
![臨界流](/img/3/9c7/wZwpmL3ETM2kjM2MDMxcTN1UTM1QDN5MjM5ADMwAjMwUzLzAzLyUzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
對緩流,,,,相應於曲線的上支;對急流,,,,相應於曲線的下支。
![臨界流](/img/1/81d/wZwpmLxUTN1UjM5QzN0YzM1UTM1QDN5MjM5ADMwAjMwUzL0czLxQzLt92YucmbvRWdo5Cd0FmLxE2LvoDc0RHa.jpg)
![臨界流](/img/3/848/wZwpmLzITM1UTN0MzM3UzM1UTM1QDN5MjM5ADMwAjMwUzLzMzL4YzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
![臨界流](/img/9/e47/wZwpmLxIjM1MDOzIDN0ETN1UTM1QDN5MjM5ADMwAjMwUzLyQzL0MzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
![臨界流](/img/a/f13/wZwpmL2YTN4cTM0cTOwcTN1UTM1QDN5MjM5ADMwAjMwUzL3kzLxYzLt92YucmbvRWdo5Cd0FmL0E2LvoDc0RHa.jpg)
以、分別表示臨界水深()時相應過水斷面面積和水面寬度,則任意形狀斷面臨界水深計算式為
![臨界流](/img/9/e47/wZwpmLxIjM1MDOzIDN0ETN1UTM1QDN5MjM5ADMwAjMwUzLyQzL0MzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
![臨界流](/img/6/ee2/wZwpmL4czM1YDM2UDOwcTN1UTM1QDN5MjM5ADMwAjMwUzL1gzL2QzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
上式為的隱函式形式,需試算法求解。對矩形斷面的臨界水深計算式為
式中,q為單寬流量。
套用
![臨界流](/img/3/9c7/wZwpmL3ETM2kjM2MDMxcTN1UTM1QDN5MjM5ADMwAjMwUzLzAzLyUzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![臨界流](/img/0/a24/wZwpmL3ITO1UDNxQzM3UzM1UTM1QDN5MjM5ADMwAjMwUzL0MzLyEzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
臨界流態很不穩定,由曲線可知,斷面比能()稍有變化,將引起水深的較大改變。由觀測知,當接近臨界流態時,水面形成不穩定的波狀。由於渠槽的糙率、過水斷面、底坡或泥沙沉積等的變動引起能量的微小變化,都可使臨界流態產生上述波狀擺動。因此,在渠槽設計中,為了保證流態穩定應當改變底坡或斷面形狀,以避免發生或接近臨界流態。