swimming pool

[logistic_guy]

here is the question

The water at $\displaystyle 20^{\circ}C$ in a $\displaystyle 10$-m-diameter, $\displaystyle 2$-m-high aboveground swimming pool is to be emptied by unplugging a $\displaystyle 5$-cm-diameter, $\displaystyle 25$-m-long horizontal plastic pipe attached to the bottom of the pool. Determine the initial rate of discharge of water through the pipe and the time (hours) it would take to empty the swimming pool completely assuming the entrance to the pipe is well-rounded with negligible loss. Take the friction factor of the pipe to be $\displaystyle 0.022$. Using the initial discharge velocity, check if this is a reasonable value for the friction factor.




my attemb
i think this question can be solved by Bernoulli equation
the density of water isn't given and i can't assume it's $\displaystyle 1000$ because there's temperature involve over there
what should i do in this case?

 

[khansaheb]

here is the question

The water at \(\displaystyle 20^{\circ}C\) in a $\displaystyle 10$-m-diameter, $\displaystyle 2$-m-high aboveground swimming pool is to be emptied by unplugging a $\displaystyle 5$-cm-diameter, $\displaystyle 25$-m-long horizontal plastic pipe attached to the bottom of the pool. Determine the initial rate of discharge of water through the pipe and the time (hours) it would take to empty the swimming pool completely assuming the entrance to the pipe is well-rounded with negligible loss. Take the friction factor of the pipe to be $\displaystyle 0.022$. Using the initial discharge velocity, check if this is a reasonable value for the friction factor.

View attachment 38962


my attemb
i think this question can be solved by Bernoulli equation
the density of water isn't given and i can't assume it's $\displaystyle 1000$ because there's temperature involve over there
what should i do in this case?

As I read the problem statement, the temperature does not change during the flow of fluid - so you can safely assume the density of flowing water is 1000 (units?).

You'll need to use calculus to calculate the time required to empty the tank - since the water-level will be constantly changing (hence the pressure will be a function of time) .

 

[logistic_guy]

As I read the problem statement, the temperature does not change during the flow of fluid - so you can safely assume the density of flowing water is 1000 (units?).

You'll need to use calculus to calculate the time required to empty the tank - since the water-level will be constantly changing (hence the pressure will be a function of time) .

thank khan

the energy equation
$\displaystyle \frac{p_1}{\rho} + \frac{v^2_1}{2} + z_1 g = \frac{p_2}{\rho} + \frac{v^2_2}{2} + z_2 g$

it's usually written
$\displaystyle \frac{p_1}{\rho g} + \frac{v^2_1}{2g} + z_1 = \frac{p_2}{\rho g} + \frac{v^2_2}{2g} + z_2$

the question involve friction so i need to add head loss term in the equation, $\displaystyle h_L$

$\displaystyle \frac{p_1}{\rho g} + \frac{v^2_1}{2g} + z_1 = \frac{p_2}{\rho g} + \frac{v^2_2}{2g} + z_2 + h_L$

$\displaystyle h_L = \frac{fLv^2_2}{2gD}$

i'll chose the pipe as ground so $\displaystyle z_2 = 0$ and the surface of the pool as $\displaystyle z_1$
there's no velocity at the surface of the pool so $\displaystyle v_1 = 0$
pressure at pool surface equal to the pressure at pipe exit and both is atmosphereic so they cancel each other

$\displaystyle z_1 = \frac{v^2_2}{2g} + \frac{fLv^2_2}{2gD}$

is my analize correct?

 

[khansaheb]

thank khan

the energy equation
$\displaystyle \frac{p_1}{\rho} + \frac{v^2_1}{2} + z_1 g = \frac{p_2}{\rho} + \frac{v^2_2}{2} + z_2 g$

it's usually written
$\displaystyle \frac{p_1}{\rho g} + \frac{v^2_1}{2g} + z_1 = \frac{p_2}{\rho g} + \frac{v^2_2}{2g} + z_2$

the question involve friction so i need to add head loss term in the equation, $\displaystyle h_L$

$\displaystyle \frac{p_1}{\rho g} + \frac{v^2_1}{2g} + z_1 = \frac{p_2}{\rho g} + \frac{v^2_2}{2g} + z_2 + h_L$

$\displaystyle h_L = \frac{fLv^2_2}{2gD}$

i'll chose the pipe as ground so $\displaystyle z_2 = 0$ and the surface of the pool as $\displaystyle z_1$
there's no velocity at the surface of the pool so $\displaystyle v_1 = 0$
pressure at pool surface equal to the pressure at pipe exit and both is atmosphereic so they cancel each other

$\displaystyle z_1 = \frac{v^2_2}{2g} + \frac{fLv^2_2}{2gD}$

is my analize correct?

No!!!

 

[logistic_guy]

No!!!

then guide me

 

[khansaheb]

then guide me

What kind of research have you done regarding leaking\draining pool tank ?

 

[logistic_guy]

What kind of research have you done regarding leaking\draining pool tank ?

i find the Bernoulli energy equation added to it head loss term $\displaystyle h_L$