Welcome to main academy.com in fluid mechanics, let us discuss velocity of approach velocity of approach is defined as the velocity with which the water approaches or reaches the wire or notch before it flows over it. Here, the velocity of approach, then an additional head of h, a that is equal to VA square by 2g velocity of approach. What you call v a then v, a can write in terms of head that is then h equal VA squared by 2g. We converted in here. Now when velocity of approach that means it is. Acting on the water flows over the notch, the initial height of water over the notch becomes h, plus h, an already initial height is h. Then the new initial height has become h, plus h, a can put it small h a. Now the velocity of approach VA is determined by finding the discharge over the notch or where neglecting velocity of approach then dividing the discharge by the cross-sectional area of the channel on the upstream side of the where or not the velocity of approach is obtained mathematically VA. Velocity of approach q discharge over here, notch then area of channel.
This velocity of approach is used to find an additional head of h, a v, a square by 2, g, again, the discharge is calculated. And above process is repeated for more accurate discharges again. The discharge is calculated by above process that is therefore actual discharge with using velocity of approach. Also, you have 2 over 3 q, equal to over 3 c d. That is coefficient of discharge length of channel and root of 2g into h that is you can. Put it velocity of approaches here with velocity approach, h 1, plus h, a power 3 by 2, minus h, a power, three by two this formula had to use it to find the actual discharge with considering velocity of approach also now let us do one example problem. Regarding. This concept water is flowing in a rectangular channel of 1.2 meter wide and 0.8 meter deep find the discharge or the rectangular wear of cross crest length.
60 centimeters if the head of water over the crust of where is 25 centimeter and water. From the channel flows of the wire take CD coefficient of discharge, equal 0.62 neglect end, coast contraction, take velocity of approach into consideration. Now you will find the area of the channel width and length that is 1.2 0.8, which is equal 0.96 meter square. Now, h1 height of water above the crust is 25 centimeters that is 0.25 meter CD 0.62. Now let us find the discharge over rectangular without velocity approach. First, without considering velocity approach velocity of approach that. Gives the formula q, equal 2 over 3, c, d, l, 2, g, into h 1, 3 by 2, which is equal two by three zero point.
Six two l is zero point. Six because sixty centimeter become point, six meters into two into 9.81 and to h1. The h1 is 0.5 power 3 by 2, which gives are zero point. Zero point, one three, seven, one, three, seven, three meter cubes per second now, velocity of approach first velocity of approach VA, equal to equal that q by a 0.1373 over by 9 0.96, which gives velocity approaches 0.0 0.0104 meter per second. That now will convert this velocity approach in terms of head that is h an equal VA squared by 2g.
That is 0.0104 the square over. Now, this one q by a that 0.1373 over 0.96 equals 0.143 143 meters per second. Then v square by VA is 0.143 that is square over 2 into 9.81, which is equal 0.00104 meter.
Now we will find q by using discharge with velocity approach. Now, discharge with considering velocity approach that is equal q is 2 over 3 q is 2 o, 3, c, d, l, into 2, g, into h 1, plus h, a power 3 by 2. Minus h, j power, 3 by 2. So we'll use the calculation that is 2 over 3. So it is 0.62 into length is 0.6 2 into 9.81 h 1, plus a that is 0.25 plus 0.00104 that is 3 by 2, minus 0.002, one, zero, four power, three by two. Now, which is equal here.
This after this calculation, we have one point zero, nine, nine, eight, five and two this. That is point two, five plus point. Zero. Zero.
One, zero, four holes, whole power, three by two minus point. Zero. Zero, one, zero, four power, three by two, which gives zero point.
One, two, five. Seven four seven one, two, five, seven, four, seven equal zero point. One three, eight, one, three, three, eight, one, three, three meter cubes per second, which is equal one. Three eight point, one three liters per second here. Look at this, uh without velocity approach. The q is 0.1373 meter cube per second with velocity approach. One zero point, one three, eight, one double three meter key per second little changes in little increase in discharge because of its velocity approach considered we have done.
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