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A tank has two outlets (i) a rounded orifice A of diameter D and (ii) a pipe B with well - rounded entry and of length L , as shown in Fig. For a height of water H in the tank, determine the (a) discharge from the outlets A and B , (b) velocities in the two outlets at levels 1 and 2 indicated in Fig . |
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Answer» Solution :(a) Rounded orifice A : Applying Bernoulli.s equation to a POINT on the water surface 3 and point 1, we get `0 + 0 + H = (p_(1))/(GAMMA) + (V_(1 A)^(2))/(2g) + 0` As the orifice discharges to atmosphere , `(p_1)/(gamma) = 0` and `V_(1 A) = sqrt(2 g H)` The discharge is , `Q_(A) = (pi)/(4) D^(2) sqrt(2 gH)` At point 2 , the pressure is ATMOSPHERIC and hence by applying Bernoulli.s equation between points 3 and 2 , we get `0 + 0 + (H + L) = 0 + (V_(2 A) ^(2))/(2 g) + 0` or `V_(2 A) = sqrt(2 g (H + L))` As the discharge is `Q_(A)` , the diameter at 2 will be smaller than D . (b) Pipe B : By applying Bernoulli.s equation between points 3 and 2 . `0 + 0 + (H + L) = 0 + (V_(2)^(2) B)/(2g) + 0` or `V_(2B)= sqrt(2 g (H + L))` As the pipe size is uniform from points 1 to 2 , by continuity equation `V_(1 B) + V_(2 B) = sqrt(2 g (H + L))` thus , the results are : `{:(, "Orifice" , "Pipe") , ("Velocity at 1" , sqrt(2 gH) , sqrt(2 g ( H+ L))), ("Velocity at 2" , sqrt(2 g(H+ L)) , sqrt(2 g(H + L))), ("Discharge Q" , (pi)/(4) D^(2) sqrt(2gH) , (pi)/(4) D^(2) sqrt(2g (H + L))):}` |
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