Please solve the q 195?
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"Why is neutralization a double replacement reaction?"
First of all, only (1) & (3) can qualify as answers on the basis of dimensional analysis.
Apply Bernoulli's Theorem to the holes, where #2 is the lower hole:
#(P + rho g h + 1/2 rho v^2)_1 = (P + rho g h + 1/2 rho v^2)_2#
#P_1 = P_2 = P_(atm)#, and #(h_1, h_2) =(h, 0)#
#implies rho g h + 1/2 rho v_1^2 = 1/2 rho v_2^2 color(red)(implies v_2^2 - v_1^2 = 2 g h )#
If we now think what happens in time #delta t# at each hole of cross-sectional area #a#. A small volume equal to #delta V = a * v \ delta t# is emmitted from the tank.
So for that small volume:
- #delta m = rho * a \ v \ delta t#
and it adds momentum, #delta p#, to the existing flow, where:
- #delta p = delta m * v = rho a v \ delta t * v = rho a v^2 \ delta t #
#implies ((delta p)/( delta t))_(t to 0) equiv dot p = rho a v^2 \ #
This is significant because Newton's 2nd Law says that:
- #sum mathbf F = mathbf dot p#
The force imbalance is:
#F_2 - F_1 = ((dp)/(dt))_2 - ((dp)/(dt))_1 = rho a (v_2^2 - v_1^2)#
#= 2 rho a g h #
