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Raptor11122
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1. The problem
A funnel is in the form of a cone of semi-angle alpha and is placed with its vertex downwards. It is filled with water to a depth H and then the water is allowed to flow out of the funnel through a small hole at the vertex. If the stream of water has a cross-section of area A, and the velocity of the fuid in the stream when the depth of the water in the funnel is h and the rate at which the water level is decreasing is equal to U. Show further that:
## U^2 = \frac{A}{ \pi \tan(\alpha)} (\frac{2g}{h^3})^3 ## (Equation 1)2. The attempt at a solution
## A = \pi r^2 = \pi h^2 tan(\alpha)^2 ##
as
## tan(\alpha) =\frac{r}{h}## for a cone
##uA \delta = UA , u = ##velocity of fluid coming out and ##\delta << 1##
using Bernoulli means that
## u= \sqrt{2gh} ##
from this you can show that
## u^2 = \frac{A}{ \pi \tan(\alpha)} (\frac{2g}{h^3})^3 ##
The problem is I have a ##u^2 ## instead of ##U^2## as asked for in the question. What am I doing wrong?
A funnel is in the form of a cone of semi-angle alpha and is placed with its vertex downwards. It is filled with water to a depth H and then the water is allowed to flow out of the funnel through a small hole at the vertex. If the stream of water has a cross-section of area A, and the velocity of the fuid in the stream when the depth of the water in the funnel is h and the rate at which the water level is decreasing is equal to U. Show further that:
## U^2 = \frac{A}{ \pi \tan(\alpha)} (\frac{2g}{h^3})^3 ## (Equation 1)2. The attempt at a solution
## A = \pi r^2 = \pi h^2 tan(\alpha)^2 ##
as
## tan(\alpha) =\frac{r}{h}## for a cone
##uA \delta = UA , u = ##velocity of fluid coming out and ##\delta << 1##
using Bernoulli means that
## u= \sqrt{2gh} ##
from this you can show that
## u^2 = \frac{A}{ \pi \tan(\alpha)} (\frac{2g}{h^3})^3 ##
The problem is I have a ##u^2 ## instead of ##U^2## as asked for in the question. What am I doing wrong?
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