Question:
in the special case in torricelli law when p is ver very larger than atm. pressure ... why do v neglect root 2gh ... wht cant we neglect atm. pressure itself
Answer:
By Torricelli theorem, we have
v the speed of the fluid from a narrow hole v = [ 2(P-Pa)/ ρ + 2gh ]1/2
In mechanical properties of fluids part 19 video, there are two cases which are discussed at the end.
- If the tank is open to atmosphere, then the pressure is nothing but the atmospheric pressure. Hence, P – Pa becomes Pa – Pa which is zero. Hence, v = √2gh
- If the pressure is very large compared to atmospheric pressure which means P >> Pa. Hence, P term cannot be neglected as it is large and gives a significant value.
We can neglect the other term √2gh only.
As P >> Pa, we get P – Pa = P Hence, v = √2P / ρ
In the question, why do we neglect root 2gh why cannot we neglect atm. pressure itself?
This part is part (b). Let us suppose we have contribution for v from two terms say one is 10,000 and the other is 0.5. Then, we can neglect 0.5 but not 10,000 as it is a large value which contributes to the calculated value. Hence, we cannot neglect Pressure term as P is large
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