:Problem with a cylinder tank and a nozzle

[Co2]

urgent :Problem with a cylinder tank and a nozzle

Hey guys,
I have been given a problem and I really want your help cause I have some doubts:[/B]

A cylindrical tank 1.52 m in diameter and 7.62 m high contains cottonseed oil having a density of 917 kg/m3. The tank is open to the atmosphere. A discharge nozzle of inside diameter 15.8 mm and cross-sectional area A2 is located near the bottom of the tank. The surface of the liquid is located at H = 6.1 m above the center line of the nozzle. The discharge nozzle is opened, draining the liquid level from H = 6.1 m to H = 4.57 m. Calculate the time in seconds to do this.


- I have used bernoulli equation
(P1/ρg) +(v1^2/2g) + z1= (p2/ρg) +(v2^2/2g) +z2

- I assumed velocity V1 (related to the height of the oli in the tank) is very small due to the large diameter so i simply neglect it

- I assumed that Z2 elevation to be zero since the flow direction will be horizontal, and Z1 =6.1 m
- P1=P2=P atm so it's canceled

so I left with:
V2^2/ 2g= Z1 then I got the time= h/ V and here h =(6.1- 4.57)= 1.53 m
but though I got a unreasonable answer about 0.13 s


so please can you determine where is the problem in my assumptions
thank you... :shy:
Co2

 

[LawrenceC]

Assumptions for Bernoulli equation are ok. But...

Velocity of flow is sqrt(2gh). Volumetric flow is V*An where An is nozzle area. The tank area is much larger. Volumetric flow rate is a function of height of column of oil. What does that suggest you do?

 

[Co2]

I see, I will have to use a differential equation, but how can I relate it to my equation above sorry but I'm very confused ... thank you

 

[LawrenceC]

Write a differential equation on the volumetric flow rate equating the drop in the reservoir level to the discharge of the pipe. Velocity of the discharge is sqrt(2*g*h). The volumetric flow rate is Ap*V or Ap*sqrt(2*g*h).

You need to relate that to the rate of drop of height in the reservoir. Whenever you derive equations, always check your units to make certain the terms of the equation are uniform in dimension.

 

[Co2]

got it... thank you so much

 

[Smiley World]

Hi
Can you write the differential equation and your answer pleas?
because i consfused little.
thank