The following are the important expressions used in notches and weirs.
(a) Discharge over a rectangular notch or weir,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALoAAAA3CAIAAAA0QsegAAAgAElEQVR4nOV995cd1ZVu/zPzZuaNPcnjOIYBCVBq5dQSSq1WagVACIkgggRIYIExwcZxTLAxwTbJYMNgEyQyygQhgXJ33773Vt2qUyenqvfDV/d06XaD8cx689asx6rF6r5dt8I5397721FdvnB54fPC+9wZp6zX+DUvvC9c+GteeOOUMsLnzuXWOFX9U8f5Pi//JDUntCUUs95ar61Xxilty7v4wikjtJW+cBlL8bPLrS+c9do4hefBz0IxoZjUXBlRPbSV+MF6jQfwRfkiuJRxikvKRFa9mjICZ+JdXG6t17g7jo53x0uFz3F+x+trK3Ejqbi20rqR5xl9NeetMsLltvw1t+GZq0fHFcL5+Ap+xcOEP+G0sBF45XB0XB+bgu9i2TvuHq5pnXa57Qr301YKxfAO1Wd1udVWaitJFidpE+d0bE/HwoU7Gaek5sDWyJE7QAFrpK3Em4RXxXbipjiz+kk48N3ws8utUIxyggeLW/WUREIxnICvh0tJzXFfLKgyAmeGRSyXuwKOsJThk+pfqwDFFzvfun0yTgBclBFVEHfs5Wi4VK9jvXZ+5GGqEAmSNvqCY8HlHDBVhb/jBJfbriompOZh27QV+DkAn0sqNcclAJrqkgXQjI3NyqMDMdWlN06RLC73r3A+d2FrO1atujdBA7nc+twFZYObWqedt7gREFNdI+NUeDZtJaEtPEAVLqPXtAMu4a9ScyYyyolQDPfFLUbvcRVPASL465i723GF6k3x7tXL4mdlBOWEiQy7OeYzVF8Nl2Ui45KGEyCKWE+puVAMj9oVhI9LSjmRmmOJKSeUE2whE1nYS+gMmIagkKsKpmNpIGdjroJ15ZYDHB1q341lEapwCdoFJxPaYiLDggZ9M7LKFUEMB06DduGSdsClio8OMahqIJdbqTl2CKuEy/r8M1WLr6xVUEUQv78ULh1kwDglNWMiw+6MqZZG38I4hecPHwa4QAtCElxuuygn+Fsw8HnhjVWUE0JbOE9bGeiIL5zUHNiCKI+YSaeDenBjmfnwK5RwqQa8hs0K0tYBu6pkVw0QHgPAh0LikoYrYLeqCAtmCJYo3No4lbE0JVEHXMa0NaPh4guHBeWSwroJxTKWMpGNCRdsTyBMuCaYwJ+FS8dThZUJHMW1TXnVuH/OEQwLeOE5QosHzh0EAIvTBTrCJSW0RWgL3AUbD4uutKgaFG0lExkTGU4OD6SMgEILoh/EK+gM6G0uaRQPN6Oa1FxbkbEUisE4KRSVmhtXbpv2ShouNJOGl9zFSW2l0IzLjAlCsjhjKQDNZUZ5CpkodY+TxillBYR+BG1OwvyBX4eHr8IFS2kLq52ErZGGn7PEXmlXsi6pOWEJYQloO4SV0JbLz4FdoGtMZEyQqrEYxUPbKrCwHUf1gtrJsCzKCGk41kcZgbcOVrsD8SNwKaWXS81wqY4n0b5tUnNnve4iWQzLAvnARWHRoWzGhDbAWApZmy0G6gN5hfqCIXBtf4dLmrGUZFHGYmVYxuJGcyAljZQ0KE+EyoTKhuunCU+E49yyhMVEJNKLTKZUZ0xlOleZTEnWJDRqNM6mpJGkdcqTVjIct2qtZJhkTZcrlUtmKDM0YXGcNfCzzpUpjC4U1VmSNgltBbAGp2xEoxRGeckM5ZYxQ6nO8AO3TDpBREIVibNGwmKqs5S3qCLSCzxzROot2uSSuFzlhXW5Mk5YJ32ulWFRPFQbPtVoDkhNfaGNE0ykUlOpqLbceonzleXCcekFloIZShWhiuBJwofM0EymKW9RneHAX1UutQexs7C28CurImGcNE6EXaA84ZJwSYwTeWF9oXWhdKHwDNKLLqEY1AAYDcCFX6E/gl2oWlAuKZc0SFvwNXyb9gdyA9MQdC+0i7HC51ppRrImE6lQmZCZtjxjcTMazFjMdYYdIiKhOtOFUrnMZNpMh6UXJtfGCS5JFA8pw6SmyjCSNQmNuSRCZb7QwnFmqPQCW8gtIyKRTuhCMUPjrNFoDJIshhoIL161NdKLhMUt2qSKcE0BCFwKmGgmtZS34qwxHA20aDOTqcqlsLzRGopI3eRaqMw4Yb00ThgnfK6NE5QnKWlkLIZs4AShsiStk6wJrAAuhEbCcVMYUxi8TspbRCREJJlMqSLALlUk5a1Mpvg54Enl0hQmSDJMZGCcbdAo6yUTaRQPERpxSZhIsSPWS19oUyiVS+E48NcFHeByC24fQi/Y2s8yn9j1QBirrrVth0lSEmUsDdwZWhqGTygqNZWackmkothvn2shs4zFLleiLUxQCbawkKSUt3SudK58rrkkzWjQeeXa75yShnHC5YqJNIi7LawulHA80xnVGTM0IvVGayg8P8Su6gnj0LkiIinvWKiUtxIWA4LC8ZS3Ut7imkovqCIRqTeTGtWZLaxwHLoHqgKHz7V1ktCo0RxI0rrU1FihDCs3JtdMpIRGLlfQN1ySZjwImQ5io3Kpc4VPAAvhONUZHgwrE8RDOK5zBb0SfFt4AxVao/PCQtjCkxgntOXGCcAFSBWO60J1BSsF+1ISjtwBMSGI0qFdKCcZSwOwYMiCdgHdayWNlERc0kCTA1ykZlB6XBKYlbff+uPx44e5JNpwSmOuMyISSDakROcKO80ts4V1ucpY3GicBT5crihPGs0BvHMzGkxYDNGEyReOB1UBTRAijeCGIQQSXhNntmgTexORejMdTnkLwG20hmAFsGelpdAZpBDIxorjyAvrvKI8ieIhWE+hMqkp9ikvrHFCaorXUYalpBG3ahBrWDdcvISLIoA+TFLKW8pLUxhoAm4Z5AQhj0AqAqGuahdfaKlpShpcEuultlxbrgzTlvtCm8JAzUsvdKG6ggrBkrl2xBZKbEztAlVEaAvEBS4JlzScD9+SiSwEagP/h81yuVaG5YWtDZ/asWPrhEkXXTD+3y6aMG5Z7/w/vfQ0F8TkiogkInWqCBYIMh1nDQiZsjxjcb1xRmoKtZmxmNAIkpGxOCZ15aXOVRDQiNRT3pJeQPEE7wnvXuVtJbgLowsFpGIPIOUAx2D9VMJiCDQRSSZSKB6dK5VL0BplGLRF+L8ypZwow4APyhMsBX5NSUMZVoq7LjUrwBcUBl6hRZv4EHYWT4JHBZKUl9pJyCc2oiMUCe0CuAC1MILOK205sKtzSXWWybSEC/ZYWwXtgstBcYG4jEaMa0ca4I4iyo5HCVqkY+ldO3Bc+vdea8uVZitXLV66bF6jOdBoDtx4w6be5T3zemacOPGBzmUmU6gB7DdgjjWSTgTrQ3kCiRQqg/VVhlGeUJkqL21hg+oOcAEpgRWGdgwZhuBDudyqXKpcBpYHvhJnDWiXZlLDCuq2dVdeEpHAbsJ2cElgc7H0IJWgt3lhgQxoGpcrqam2vNE4a50saY2X0CgJizOZZjI1hQE+Ut6KSB0fwixCAYCeQ+dxy6gkoPOgCqAQIJ3tWKUDRDIWt5JhIAaYlpo6r2xhARfo+FK7IPIRTDjiEAjzjaa6rs20oYcADrDuEN4JUbKOCBusmNQM+nbHjq379u22TvpCK82uumrtqtVLfv34AyZXpTekCMg/KB5+pTrTTpCsiTfUlsPwp6QRRAQ8FC8pnaCKBPMPuBDagiuHdwHcqz4k1AksWsAKEQlgRBXJZGryklO3aDPOGlQRoRnhCbYTVsblCoTAOklorC2HRtGWD9dPM54SGlkvQf9J1oR19rkWKqOKSCcymeL1tZOByeFdAr0tdVtRuoQQFWVFGW410joN9wV5EuyUy7X1shQwnuA54T3AGEnHW7QJyy696Ar8FKGY4EWX0bnPCBPB3gezBRkNYfhAG6tJgBAgJlksFCU0ojw5cmQfHs7lSlv+1psvrVi56LbbbrCFxmtjLbBeUInSixZtMkkIjUjWLFU3jeBFM5FC82cizWQqvMBmw3dghppcl46GyCAegbtU1aEvnClMcGIDVrAl0gmqsxZtBtNei84202Gdq0ykLdqMSF3nylghNc0Lqw2HxWQiVYZRGhsrrJf1xhkuiXWS8gRKCCSslQw7r3yuda6ASJNrQBBaBMsC4I64915AGODBSSeoJBlLEWsFPUjSZnBoEAIujU7b+oC+4GG05cIy8H1mqMrlSM6o6klWNcpn0Zfq+dUPQQjcuckq67W2KoQIleHacm24zzWCDdpyobLt27esWr3k44/3i7a/is2AgqE6U17qQmUyBVXEF3HAhdaWl85FYWBBsOVhQeGXwmWAQoWKDhwuPDPcEKqzOGvAgy1pU9uxhHXAhjXT4eFoQBjWypqtrMk1bSY1vKPLlTYcW+K8Mla0kuGMxSlpGCsazQHnFf4Pg4WwAhdEakoVUV6CwAGg8JDLsErbDgb3HvwGSlE6wVQGxQlHGkGvEFL3hTOuVC3gLtDTsERwjpQXiF2B8ndVN7sap/osvdIBmmD+O7LqHbmM6jm+cNqIvLDwM7XleWGtk9bJcRdduGf3712usLWgdYGrYqXgFQtNlWEhSgHZxYFPlJeBfOhChahoIM7BPvrcdWSpSnwXyhY2CLfysnyqQgFzuA7oETMUKge7SyWhimDvwaugThAHA3eBGwhDTHlCaISToTLh05bc1okQSoAMwA8K1gevCeDiZ7iE0olqmjC4IyGr4wsLfUayJkJzCAgFnw6BTekEt0znqisvfF646uFz53PrvWk71ZA553Prc5tX4vphiavBbIT/x4RL4OTWKeeVdTIvrHFSqCxNmzfesOnaa69grMUlkU4gIolnxZJBM2snhWHKMGW4tsIX2udaW+EL67y2XinDjRXSlUumc4XFLfVKoWD+AyUPzj9SJEFNwsdRucIV8K2R6+TK5BobWbpglqtcKi+ZyurNwQndl0yfOfkf/vnLq1YvGXfRhdNnTv7W+d+4YNz502ZM+tu/++u//bu//uZ5X//meV//xre/9r/+5q++8e2vXTxh/CUTL5o1Z+pXv/GVL/393/39P33pG9/++tXXXZHQSDvBNdVOlvC13OTa5RYExRTG5BpHGbbOS0BrJ307hSc1P3X66ODQKWWENiXxME4ZJ0jWbDQGnNfGSeMk5WmzMSA1M04KzWC+sYZdee6KwlePPHd57qRk1qqi8NYqpTg+xMnGdHKaajarBFP7/DEP563U3HlrrCJZbKzatGldz8LZAwMnjFXalHndEBDCuwW2FLJovppC86Wv7rz9HNb1OYd1uoxx5w4Z7M8/RudB8YRS8z27X/jW+d964/UX9u3b3UqGT5788JNjBw8ffvvw4bePf3L4g8Pv7N+7++DBNz899v6H7+89cODNw4ffPXr00CdHDx848Ob+/W8c+XD/+4fe3b//jePHP7ROoyoNu24rhWNB/MInYGMjYglKaqS28qEHf7hi5ZLe5Qs3bFjVajWQbZaKG6tuv33bLTdfh9TNLx7+ycJFcxctnjtrzrRPjh0OBUNlAcOYcHFOe2+0FloL7421Ch/ih/wzFu6Lw0Ub6QuntHDeckHv/t5ty/subbUa1mkuqfMjZVOI7GEbAo8GJihP4Z2VJ1jFRAbQcEH/Uqyg/s15m7HU2HPidZ8Jr0rSAChBfNLn7tVXnp/cPTElDZ9rypPAH8u8mMy4ID7Xxo4k2OEHSMW1kSGljJcNnkQVB6OxErKYI8l/p41TztvDh9/t61v0/LNPbNly2ZSpk6BsUCTEJd24sR8czuV2ed+lN2+/9vv33bFp07rrr7+K8iwoXZ+7rrGl32nndJ477w3+j6MovHPajJLdvxQuPneIAistfvD9Oy+/fPWRIweUESmJfO5+8P07T58+hiiIaVfThWUFaCgnHu6upMicG6sgiIFu/2VHXmbNnLdKiy9yhZCVxD4Zpygj2Ilbbr7utttu0pZLRRH4ggOIyBChEYIrqPrAkweNi8UxTlmnsd/4uWoog2YN6xOIl62UECGkju8i6fHxxwc3bFjFJYWsSsU/OXr4O9/Zrq0UkikjDh16xzpNaGvduhVz5s04dOAtJIlRpNdVRUM48twpxQfOHD+4943HH/n5rduve/nFp2nWCgrmvwgXYxViALfddtPX//Xr02d2r1+/8sKLLsTP4y8Zbyr1s9CxQdmUCl/xcnchZE4naROVAz53KYm+IFsPB/xMLErGUpLFf/Yr1U3CYyC9b72+7babDh9+F6olYzGXRFturAjpGKWZy0uVYNu1Iq5SOIyXglCBDlbri6up0Kp2CUrFtYt+UhIlSRNak5D4u9/dsWvXzXnhsUR54S+7bPVTTz6SFx5PDtcpY+mmTetWrV6GohRQ41K7dGDFOT00cHLbDVvWrO594lcPPPvkr55/5vFNG9fedP3m0yc/xmb/F+EC/L70wlPTZkxZcOmcGbO6Fy+Zt2Llknk9M/tWLH7t1d+XZTdtMQqcNAAohNf27H5h166bv3fXzu9+d8fu1/7QjGrXX39VbfjMX6xdCqe0GK6ffebpR2+/fdvZM8f/7PmBNvl2Hp6JzFjFJV3Wu0AoZr1EWMV51YwGg58vVAb3FRzLtSu/nLewxage8YULdZyoQBq9zr5SBo8rYF+x5cgWGauMU5QmGzf2T5sxZfPmDZQmsHHNqPbN87555MP91WittjKO6319i1584UnrNMni8FRdgdjCAFmrzpw6eunCORdfPP7s6WOcEWNknrs9r/x+avekO27fTrPWaO5i21VkkM68cGDHuGBVaYEe+dyCc2Ss5B8IyXRW6FWJpNOEtvLCl3Bx+oPD702cMmH1mt7t26+Rit/9vdsumjC+e9qkC8ZfmLF0dGFeB7I7XgFltjt33jh77vSly3pqw2ectwiG4moBEyHXkZ9bhV+aJ28PHHhzw4ZV2kguiDJs92vPL1k69x+/8vd/+6W/2bJl/fHjh40TSVp3uXa5hf0tLVFuCW3hvtj1jpBE4DG44xuvvzSvZ+a8npnXXXflv3z9Xz499j6syffvu+PiCRddeNGF8xfM2rHjBql4FA/7wikj7r3nO73LF+7YcYPLLRPZKy8/N7l7YqMxiAygcUppYZzas/uFG2/YjIRgKbS5ywvfFYittco5PXj2xLy50+fMmX782PugL0pxzkjSakydOmlBz6zDB94aU7tYV1IznzulufdGKe69kYJmJO6AS3j/kbXOXVjuIDF2VNklQGadfu7Zx+f1zLz88tWN5hAIo/OW0uTqqy/vXb6QMjJmyPFz4OLRvKLFxo394N3AcZa1gBI0ggQoh0hXCDWVi+v0PXffvmvXzVJxbfiPfvjd1WuW7tq17bFf/Wz23KlLl8278so19cYZ62UU10BWnLcki5UWlBMgBrIXtioc0Ebh1bikt968dXL3xGuv3fjxxweVEWBv9cbAmv7eeT0zn3v2cZLFUvEyOaMFpcnqNb2TuieABd53767HfvVzJAchElLxP/7HM7PnTm9GNW0kXg1R/tIzkoLmudNa1IfPXrZ+Ve+yBUc/OgAAFYWXggJJixfNXdG36NWXfufHSjrC2YGNoLTlnDZGCp4ZI0drF1exMqEc2lZqtjt8RdwCq5kX/je/frivb9GsOdOiaList3KK0JbS4kc/uOuBn/8AQOwIOn8+XPDJBx/sXd536cYr+jOWwt5bp6N4GHSvI4w0WsXiGZb1LrjjjluUEVLTmbO7Dx58A5mjodrJ7mkTV6xc9Ifnn8gLmxc2LzyK+iC7UnNIXTOqgc6HpRi9JkgDr1i5ZFnvgt8981jgQNZrksUrVi4Zd9E4uD8AJWhvK2ls2rTu1lu2gtvu2HFDXngkHbGSv/zFT+cvmAUa9/qeFw8dekcoFl68NEbYzr1vv9a7tOeKy1bTrAXzxBnx3hgjjZHdUyYuXTzvlf94djTVRXQktClZqzgjwQzBG+8wRr4Sbi8VQD6yl+FPYWlgBVxum1Ft1pxpPQtnP/XkI1gLCAoTmXX6nbdfyQuPWpwxEfNZcMFOPPP0o7PmTLvn7tt94VISKS2wcCmJABc4+aNtXLiIkKy/f/lzzzyekihJ6/v27S7rnrxiPP3N4w8u71vw8EP3UxpbL4VkpU9bOJLF1mnGM6XLMtZq7UdQsSGsYpxqNAZvumnLrDnT9u7dA3hZr41VL77w5NJlPffduwtQUFo89PP7p8/s/u4dt954w+bt26/BySdPHunvXx4auIRkzag27qJxl0y8eNacaavX9E6YdPGrrzwPKcUudOW5i5u1ovCMJgsXzJ41a+ofnn1CaxGcIK2FUnxo4OTU7kndUya+9IcnR2uX73xn+/r1K6+++vLFS+bdeuv1s2ZPXdu//I7bt9+49aof3LOLZq0xtYtrdzCBBIS6aNMuEK6uFEy78/Z7d+3sWTj71luvzwtPOQlmgvEsb5cJB6xUr/ZnjRET2aZN62bNmfbwQz/656/+8//+8v+eOXsq7h636iWpyp2tlBf5SoAb4vvqK8//07/80wcf7LVeI6eIYH8UDWnLf//c473Le955+09KM1+UGosy8sP77+pZOHvhormbN294+KEfPf+7J9J0DOcO+iP8cOLERz0LZ2/evCGKh2GOuaSMZxeMv3B536UffLAXIZO88KdOH7322o3XXXdlvTGAogBt5FDt9JnTx0Y0Ze4oJydOfLR//xvPPP3oKy8/d/Dg29rIqgx3IQpinU5ajaWL503unkhIBAsFL8k5XRR+98vPL+9duHTxvP3v7ilGCdZbb/zp0V/++zNPP3rHd27+3TOP3bnrlttuvWHrNRu/f+8dO2+5vtVqIKWQh+4TuIW5G4mR5GU3WvARwNJdu0UDKY+4VZ84ZcL0md3vvfMarhCq4Kr1tkIyYxVcSutUmbtor13eXnrTbuvybZ9r1eplc+bN2Lnzxtf3vPj9++4Yf/G4vr5FsP3GKawdiBoiIuF1gtA/9OAPp06fbMpGO46CS/hBUtNt2zbffvuNyKdySazTKYmu3nLZRReP3/fenk+Pvb9l84ZlvQuuu3bjpivXhstWNWUIr2kr9+7ds2Tp/Jtu2rLntRf27H5h33t7Dh58+8nf/nLxknnLeheASAXCF9YWwBKShZp8NBOFEKhpd3FUmQA+6YJ8KCPefefVxUvmzeuZ6dvmCd4NtMJdd9y6sm/xxsvXMJqEVQsKmZAYrjlujF3RprS+1bYj3PuRX/5s/MXjZs6eOm3GlN7lCzdv3jBrzrS582es6e/tW7F46vTJ11135caN/VE8HDAEu/vRB/vWru1bv37lkSMHsN9wHbGI1mulBcKy0IucEbwFKFQ1leErZRtQVL9/7teTuyf+7Kf3Ss2NVadOfnzJxIv7+haFtABUPcoZq8i2voz6JGnz2ms3PvjA/b6MyiikneNWzXp5+vTHF4w7f9++3S5XcavmvJKCruvvW9678Mypo5DPwwfe2rBu5f333sEZMe1ng1ChYAXLKzXPC//gA/evXdt3/fVX/fQn96xfv7Kvb9GvH39o2owp02d2P/Hog2AIHRGs8Nam3cUStG/I91VZfIde6IJkG6de+MNvlyydv7zvUue11kLwDCuutTh7+tikSZesXrWMpJH3xlb66XHvA/veePH53z737OPPPP3oq3987qknH3n+d0/89olfPPXbR157+XmSxR1x61f/+Nyq1cuuumr9mv7e1Wt677zz1nXrVqxe03vTTVuW9106ccqEhYvmzuuZCSaLNUJY79VXnr/mmivWru07ffoYdC+CeEAVZQRCwCVVisOe1ofPvvPmy+8ffLuoRIO8N2ih4oIiMsEFvfrqy/tWLD5+/EOlhdJiYODE7LnToSoCLYOLq40EEaachF0EjPr6Fr304lNQdcow6yR0STMavOqqtQ/8/D6p6IkTH6BMR2uxfu2KvuWXCp5Zq6xVP7zvzmVL5h8+8BZJIyloyCdDoyAIiVgl5aRn4eyJUyZ8+skHyHa53HJBb95+bd+Kxa+8/BxWJsR/A42zlZ4jXel0DpoyWH8zqm2oyxcOEjZcPzuvZyaESWsBeit4phTvX9M7Z870H9yzS2vRioarRBXabNOmdV/9xle//I9f/srXvjJz9tQLxl1wwbgLpk6f/Fd//VffvuC8o0cPhecLlAJsgHKSpE0uKCExyeI0jRrNoXpjYKh2Ok0jJjLQAnBMl9u9e/f09S0af8n4kyePJEkTi4i9gWRQXhbhBv7+4eH3Zs2a2rf80pARg5ENtBHhvmMfH5rXM/OKK9Y0oxr8WBDGyy9bjVBE6W250jJqKz85dvi993YjVwXd1mgOLVk6H56acco6yVhLqIyJdNeubXfeebPSTGmWZRETqbbce3PlFf2XLpzTqA8YI19/7YWpUyfd+73b42bNWkXSCFkwZMSqxVzayCNHDoy/eNydd94KtYEIVtSszZ47fe78GSdOfIQYnTt3SkMHI7Tn9mn79iSAEOMYAy554RHr3b79msndE997b7e1SgqqFNda3LztmhV9i354352MJsZI57Q7twg3UI0yhuY0+owoI0nSVFp0dP/CzcH241tlMBGCGwp+rcK6w6iBu5w9e3zWnGn9/csPHXgr1J9ar6XiXNCf/PjuwaFTuDtewVr1zpsv98yf+fDP7++ILKMXM8jue+/t7lux+PFHHyjFV4uVq5YuWjy3lTSUFlxSksWBSMVx/Y47bpk4ZUL3tElHjxyEPWI8Gxw4Obl7YhmwYWlogHrm6UeuvHINyZpINCKXJFQmJVOKb71m4wUX/tv2m66eNm3yLduupVnLGKm1QKIHETyoroylraSBcqef/PjuOfNmnDjxEcgH5YRk8SsvPzdx8iXXXrsxfKuaXRqT4Hd4FWWFvy+9kDHgAs2jjPjww33nXXh+34rFJ49/RNLo5PGP5syZPnXqpNrQaWsVXkMpDj4fHA2gpKRRRqYkwtpZp7mg2I+OiBnUYAjXBtyE+p2ghMoXzh2ekPFs+7ZrpkydtGTpfEqTMiNohPP2wX//wdTpkykjSdrMWJrnzlpljLvRF08AABLBSURBVHzkoR/3r+mVknV4Z1E8/KeXnkWwgYns7bdenr9g1muv/h5y/Nivfj5jVvfPfnqvbk9qGQnYe/vOW6/ccvN1P/nx3ct6F1x22eq4Vcf67tn9wvfvuwNvlxceDWk/++nd/f29SVJHNV3G4t7lPadOfeRzLXimtbh1+3XLlsz/6P29A2eOO6eh0bUW1pY180hFRfFwK2mQLEZMYemynjX9vbXhM8YqqNiMpc88/WjfisVvvP4SIB40aOCwo0OXgc/6dks5yr8/0xjlhQdD1Fa++srzc+ZOnzjx4qWL582ePa1/Te+B915H7AS5AjCyjuB0R3ggwKiDEY8EQNtkG7+GNh9onZAQrl4BGQZlhJBsw4ZVM2dPveXm6w4deufdd1/bv/+NXbtuXrFyyZEjB1g74X7y+Eevv/bCjpu3rl61rHdpD4LXwArs0fbt13zr/G999NF+aJdbb9k6a860fftep4ycPXt869ZNGzf2nzr1sW8XIwNYQUH63B05cqCvb1HPwtmNxiCkf926FTt33hgoJMmahw69NW3GpDX9y37x8A+fefqRe++57fLLV61YuejMmaOUJ8bIx3757yv6Fr39xp9qg6fiZk0KKiVDeJMzAo1yxRVrNm/eUBs+w3gWxcNS83ffeXX+glnr168cHDxJshjmqdEY3Lbt6osmjE/TCMkE1w4325Fa7jY4cueLkSkIYWtg06ujW6rx965AleO4bp0+efLI8uULf/ngj0588mHSaoDBwNg36gOcEYTvxkRDR3ijelSjILbdVg0PKzT4pCTCa4DYBtc0RKWge3zhGo3Bo0cP9fUtmtQ9YVnvgp07b/zTS88i64HjpRef+urX/uWpJ37xyceHeubPfOv1PwLxSHcgYP3gA/ePv3jcmTOfCsnAXX54/119fYsuu2z11q2b/vTSs3FcR4o/IDVIalkK7vQzTz+6bt2Ku793m7EqJdGa/t5XXvqd9RoJwiNH9t1001XLeudv2bL+wosuOH/cedu2bV6x4tJ9+3ajsljw7LL1q6ZPnzK1e9LMmd1LF8+7dsvlw7UzzumMxM5rodhQ7fTqNb1z5s04c/pTyohQ7Mor15534fnd0yZdPOGirVs3IZt4+vSx5X2XfvuC82bPnb5w4Zwzp48h32krkyKCMQ3x36qywa9ITMKlrco5XrkLfgQ27OjRQ8t6F8yc1f3IQz8+fuz9Rn2gWR+UktUGT/3phacmTrzYe4MEUEcuowMcow9XSbWXCcU2Z4TmaLUaYCfaSFTTuXOLw+Hr5oUntBVSkvCiYSbSNPK5I7Tlcrt2bd89d92GFNiFF15w5IN9sE3Bl4aCLD1/LUIcKG7VEZCAF4rmkuBNBNWCOLLLLeVkw4ZVPQtnD9VO//E/njnvwvMHh05RTlDCgnZXJKV9XjYyovzFOMF4uuPmrTduveqj9/detn7VZetXXXDhv02bNnlt/3IpqBSUkBihhIGBEwcOvJmxFAFrXzh0D6G5x1iFZHijOdSMaoNDp37z64eH62eryj6sP4ACNZNXxsIFAgDTHLqCOsBUGiOpOfzGvr5FkyZP6J4y8bzz/3X1qmULemZtuWrDokvnruvvO3XiCDTkmOrkc1TLaMQIybig6H954rEHb7xhc9+KxVu3bqoNnwGfrz5u0O0IgMJUw+IECgy3Fmj74IO9y3oX1IZOS8nuuH37+rUrWtEwclhIflU9IxRzIOYGJmScQmI8VMwjKOcrM1RcZYTW3r17ehbO3rbt6t/8+uGNG/uRZuKCCsmUZiiThnPEBUGlS8ZixtPv3/ed+fNmNOoDUlDOSJ67gTPH77nrtgU9swbPniBpxFjKeMZ4JjWPW3XICThckjaZyFISRfEwNlhpQUgMzlGOX8ni0IcWKhJD7wjoeYhpBXJDaAsnBD4aLMMIXBjPsPo+d2kaHdr/5pVX9P/bBefPnzfjvru/06gPJK0G0o157uxYUzw+HzFh1+G0O28bjUGfu+/dtXP8JeMvmjB+4uRLZszq3rx5w5EjB6TmYfRX0JzIw6GuQBkRwt7InyGwBh/4mmuumD6zu9Vq7H93z+ar1j/9m186pwPVDWwX83/A0327UDeMKIPax1qHEgvTLs6y7bEGuOl99+5avaZ34pQJW7ZcBqca2pvxNG7VjBOo+LdetlrDQmaNxlkuyW07rp83d/rhA29lJAZfacX1OXOmP/LQj/PcNeoDH3+4H4LOJUXwvtEYlIq3FyRFLD8YnbhVR4gLQ/maUS0lUaMxmJIIzWnAEBqskOMLMAriQWgrioervUj4K07usu1SlbKT1khtZQhahJqVUOQAd6NaFjmaP49xVNgWDkJjLrMdt2597ZXno6h29uynG69YPf6Sce+//y4TRFmB0nZfOJNr7VWSRRqDM3MlNNNGcJm5XKNyXWqWsdg4qQzfufOGhYvm9Pf3Llu+YNrs7mkzJr9/6G3rlbJCGS4UZTKjgnBFuaIY+KO9YjKjkgjDUMovDU9IM6UxV7TsQPBKWE4FQVE+FSRKhrmiQrPHnnhgyvRJ3TMmv7v3Na4okxmTmbJCGKadEJoKwxLazHiS8aQeDUStWiutc5X9+0/vXbBg1vp1fdtu2nzj9Vddf92Vzzz5COOpMYLxNIprhMZCYQJBlpKm1ExqlrGWcZLxNGMtJgjK94XKGo0BkkVSMW2F1KzRHKzVz0TJMFOZsqKVNRPSbGVNZYV2kkrCZMYVhenU7WZCyGoYFBoi9UBMqV1C4BIoC1iB3g5VdmUJlRuhSJ9FdUcrm2ruw3qFRpu8sFwQDBTZsWPr+vV9hw684bxKWdnMjLEu6AELfZ3SC1MplkY3L1IzGP/x05987/FfP3Dw/bdv2bn12In30b2Mlhx0iaLPiogEnaroa0RrIG5aHbODluOI1NHFGEbO6FylvNWIhwhPrrpmwz987R9tYTOZRqQuLNeFQmsSWqbLW+gsYTEGwKARyReaS8IFsV7GcQ3dnKFPL0nr1ku8JqER2hzBh2rDp86cOYrQDup/MRwJDYhMpBmLo6RWi85iDACmT8RZAx0wulBUkZTGiJeG5J2tzPXwiNpVUlddrt1XFvxy5201vYKK7lDvXaqcUB3+xY4OuAhFhcq04SFy1UqG1/QvW9O/rJUMa8tT1kJ7FVo40eeCxmB0XnFVjg+KW7WMxWj3MlZE8RCGMZlcZyJFP5UwDD2b6OlCv/TpwU/R+ssqU3QwVAetgTgtkylanNC5HlpxmaEJjXDZFm3uefM/7v3BLm6ZsDxhMVMZlSOzg8o2RElwfTwV1xQd0Ulaz1jMRApkYLO15fXGmbhVwwwYbD8SkygXR29sqOZM0vrg4PGMxagIhu1jkgCXQd7QOBfGjrTSBmprgvuJMA+iKiFWrtrjnro6iip8u9I29JEALqHqxXuDMFGVBP0ntEtof8cyXXPNZd3TJu7ceX2S1plIheXcMoznCMNFgm7glklD0QcZWjWTtN5KhoO8ZjLlmiYsVr7sUcUBzKFZH3uGOQ/oRETjMYQPn6CNNPQJo6sSWsfkmvAkk+lg/VQmUsKTT05+IJ3AcIYwcQlA17nCDoWpMzpXQmVRPBTFQy5XaDVFjyO6X4frpzE4KIxOgiSUjdY8SUmDiRTl4lE8dOjQWxA/tDpbL2V76gy3DOMa8F6Yvia9SEgzVM2FGAHITXCatJVwI5QRXSE+E6Ijvp2zDUmWqnZx7bmxAQqfE1r+LLj4wqakQWmMHs/HHvnZhg0r1vQvW9Y7/48vPilUJgzF8B8sOppe8X+Iu8kVsBL6SUudjDklXjGVUZ2hE10YVrYYVmZwQO4xSwEWJ2FxmA8FQUxYjFkYLdqsx4MJi02uuWUt2sRUB9gXwpPhaCATqbCc8EQXKs4awjCoqGZSa6bDgB1mNTRaQ810OGWR1DSKh0jWRLQXwRiYngALX+hgdjGOBGOFBodODNVOYvwdOhFPnz4CAEFXKcOYbE80ao9Ja7SGgHv0fpfaxbTn8uXlkHN4WMg2kCyGx269LpMAeXsui7bSed3RpdbZtHZuldp/Ai5SM3AXjODyhU7S+q5d2xYvmTuvZwbJmjGpE5Fg88LYMIzBgcrBIqJzFiodc+0w64CJNCJ15WWcNZSX0okAu4AVTHLAwBiqM2HbE8JyBZ7BLYtIPSL1UhBZPBwNYEgH1VkzHQbv0U62aFNYDuujvTp+6iNhufYKNAizNkJPf4s2hxqnh6MBIhIMGUGvWmilTtI6ZpIFxEAqgCpMZkjS+tmzx4brp6FcG82B2vCpKB7KWIwTMLIlSmrNdDgMveKW1aKzzaQW5i0qK5DFBGcFf6U8xWRe+OqN5lBKIsSOu8bc7I6+xs42xy/Abcc8AmJ8bsuOilyBpkEmVq9Z2rNw5qefHGIqS1gMkjgcDaS8FWYdlIckWEcABcoZo3WQqYFkg6xg3kmY2BNnjXLwX9sqweSFoR6gJkQk9XgQE4Twa8JiaBQolVp0NhBnqHpuWZgTidZ/CHEtOhtGDYJl40aYORLGvVgnpaYgIo3G2VYyjF+xOIRGWCgYJoz8hCJJSSOKh1LSQJVnOWtDZTGpR6Rei862aFN5CUBHpA45FI4rK+B42/Z0Yy5pozlUOt5ZDJc5FLL9v4ELEwSCwlhLahpmyv3yFz9aumzeoUNvScfDFjbT4TC/KcykMF5wScJYFGhvyhMMsdGWK1/OXoDZDsiojhjCVClmqLAsAAsYBTjq8SAGVRCRNJNaozWEbcZpYJEACm4h2+NkwrRSTLuAIZNeRKQ+1Djdos1yjIgoJ4+ArIQ5PIGpdBw+b4+5wyRVw8BUhMqwFBmL4TfhmtKwsG5UZ8PRgPKydMowwMFJyknUrOWF10aUqS7aQlS6zPZr7osyxds15r7+34aL9UqoTCqakgZwow1vJcOLl8zdvHmd1NS0R3Vgm8shHY5DveuiHA8J0475WFhrUF2Xq5GhFV5gQkygyYHGhmm5IKRhBhMkD8PxYPgzmTaTGgYpwpMKjjdtz3SFUQM6YdcCs8Z1oNuaSQ0OObcs1DNgyEg5ftdLbD/GdgQYgQX7QodpmphkE9CDiWX4CnIOqr2GeDVMPMTMGNB57RXKykbYBZIquQuVRghto06ta8y9/2+AizLs+PHDq1Yv2bJlfaNxttEc2Lp144xZUw4efMN6abwsx6jkOgRgzhnTYst5TGEMKSIW5WSUQnPLMLQi0FvgBiYpjAkKM4IwWTMYkXKinc4Q9QmOaIBamHYJnYQ5nTgZ0hyG0wB55RhpQ3FxMCQ8cxhOU44MyhV+8Pk5yAA4wgCb8Gv1wBetlxiiLIFXRbimeEGsJPwyXZT9+q7dHWfbg8CqHXGhNMzhH6j574eLy/XgwPE9r/1++szJK1Zc+uV//NLEyRfPnT/9yJF9LldRPGTaE0owvwQvGaae6kIpy6pwCUOBoLShXWxhw2yc4BABLphWgr0PI6XCXQJcgAnEtYDX9uzCcmwT7gKNAkoOdJahsFyFKT3CcXhnYaCmLewI3DEdM9fVKd8+17A1UDnAVnWu82gYlUDJNbqyfWFVLuGaYQgNXhOrqouR6oCyUzMfcUr8KLjkhe/K8zzPfcdRFPnnH6O/8kUO3z5Cq2K9cXbv3t2HD79z5swxTE6s+lxhCr4tbDmvvP25ybXLNSYU+fYQfV9YXyCRKTEC1OWQRW28LI9cmlyZXLnchik6iPErK3A7k2tlBVcU/yKBbo84LBFfWFtYl5fZA20lFYQKwmQmNEOIXXvVcXHTHvOP++KfFHBeI4/hygHaynrV/gcB0FLjfFEOwDVOoU8Wr4nPXa7LD8tFUHnhnNeUp0JR63VK46g1LA1HogNLF1bVt/85FntuqWW1YCpgCC31Y/xX/Ln/xvzWF//P/+X6KeSbbKXNZ3RZlh+p6hhR2hDHoNjbCumc74YIZt5ueqqOZewIHLhK6atpt6GHah47VlXsiFcIxPuRakhT+WeJqmeGi4QUYEfdiK2UtFbfovo5ArK+0gT4Fx0d3/ofAxdfKTr5/NduL7cEUKr6/HPgUl3xisM/Uu1hzy1Nr9ZXdFTndFQPjgb0yFFhlKEE351bslRNC3/WM4ej/Nf92tWu4cFQmPGf4w9VTfM/Bi7V/bCjSo7PBQq2thyUXXLJCm38LLhU9963x7fkxci/UtkBl9GKpGOV/wxW2nvgKgWp1b2pKtGqZhq9neFAi0LAVhu7Psjb/y9wqahxXc1odJTUVFS0ApEsvesvBpfqMZJzxV/zc1ZwpGjIlzlaU5nJM+Zedjyhb1OE0caoAyWfc4z+SsCZP9duhsqe/8rxPwYuARNBzsYs2DMjDVccqgVhUBimLwKXajFXaJ4Y09D4irY37VESwZR8FsEKDCxsZGiK6ABiR1HRmNZkNFZ0pfcRpc15pVfrP73suNf/AbO4rOiS0webAAAAAElFTkSuQmCC)
where
b = Width of notch or weir, and
H = Height of liquid above the sill of the notch.
(b) Discharge over a triangular notch or weir,
![](data:image/png;base64,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)
For a right angled V-notch, Theeta = 90°.
(c) Discharge over a trapezoidal notch or weir (also called Cippoletti weir) is equal to the sum of discharge over a rectangular notch or weir and the discharge over a triangular notch or weir.
(d) Discharge over a rectangular weir, according to Francis formula is given by
![](data:image/png;base64,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)
where
n = Number of end contractions.
(e) Maximum discharge over a broad crested weir,
![](data:image/png;base64,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)
Notes:
where
b = Width of notch or weir, and
H = Height of liquid above the sill of the notch.
(b) Discharge over a triangular notch or weir,
For a right angled V-notch, Theeta = 90°.
(c) Discharge over a trapezoidal notch or weir (also called Cippoletti weir) is equal to the sum of discharge over a rectangular notch or weir and the discharge over a triangular notch or weir.
(d) Discharge over a rectangular weir, according to Francis formula is given by
where
n = Number of end contractions.
(e) Maximum discharge over a broad crested weir,
Notes:
- A weir is said to be a broad crested weir, if the width of the crest of the weir is more than half the height of water above the weir crest.
- A weir is said to be a narrow crested weir, if the width of the crest of the weir is less than half the height of water above the weir crest.
- When the water level on the downstream side of a weir is above the top surface of a weir, then the weir is known as submerged or drowned weir.
- A weir, generally, used as a spillway of a dam is Ogee weir.
- It has been observed that whenever water is flowing over a rectangular weir, having no end contractions, the nappe (i.e., the sheet of water flowing over the weir) touches the side walls of the channel. After flowing over the weir, the nappe falls away from the weir, thus creating a space beneath the water. In such a case, some air is trapped beneath the weir.
- If the atmospheric pressure exists beneath the nappe, it is then known as free nappe.
- If the pressure below the nappe is negative, it is then called a depressed nappe.
- Sometimes, no air is left below the water and the nappe adheres or clings to the downstream side of the weir. Such a nappe is called clinging nappe or an adhering nappe.
No comments:
Post a Comment