The cross-section area of the pipe shown in Fig. is 50 cm^(2)at the wider portions and 20 cm^(2)at the constriction. The rate of flow of water through the pipe is 4000 cm^(3)//s. Find , (i) the velocities at the wide and the narrow portions (ii) the pressure difference between these portions (iii) the difference in height between the mercury columns in the U-tube.

The cross-section area of the pipe shown in Fig. is 50 cm^(2)at the wi

1.	The cross-section area of the pipe shown in Fig. is 50 cm^(2)at the wider portions and 20 cm^(2)at the constriction. The rate of flow of water through the pipe is 4000 cm^(3)//s. Find , (i) the velocities at the wide and the narrow portions (ii) the pressure difference between these portions (iii) the difference in height between the mercury columns in the U-tube.
Answer» Solution :` V_1 = ( 4000 //50)cm s ^(-1) = 0.8 ms ^(-1), v_2 = ( 4000 // 20 )cm s^(-1)= 2 ms ^(-1) ` ` P_1 - P_2 = rho ( v_2^(2) -v_1^(2))//2 = 1680 PA, h= P_1 - P_2 //rhog =1680//13.6 XX 10 ^(3)xx 9.8 = 0.013 m.`