:Problem with a cylinder tank and a nozzle

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Discussion Overview

The discussion revolves around a problem involving fluid dynamics, specifically the draining of a cylindrical tank containing cottonseed oil through a nozzle. Participants explore the application of Bernoulli's equation and the assumptions made in the calculations, as well as the need for a differential equation to accurately model the flow rate and time required for the liquid level to drop.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • The initial application of Bernoulli's equation is discussed, with assumptions about the velocity of the liquid in the tank being negligible due to the tank's large diameter.
  • One participant suggests that the velocity of flow should be calculated as sqrt(2gh) and emphasizes that the volumetric flow rate depends on the height of the oil column.
  • Another participant proposes writing a differential equation to relate the volumetric flow rate to the drop in the reservoir level, indicating that the velocity of discharge is also a function of the height of the liquid.
  • There is a request for clarification on how to formulate the differential equation and relate it to the previous equations used.

Areas of Agreement / Disagreement

Participants generally agree on the need to use a differential equation to accurately model the problem, but there is no consensus on the specific formulation or the initial assumptions made regarding the flow velocity and volumetric flow rate.

Contextual Notes

Participants express confusion regarding the relationship between the height of the liquid and the flow rate, indicating potential limitations in their understanding of the assumptions and the application of Bernoulli's equation.

Who May Find This Useful

This discussion may be useful for students or individuals interested in fluid dynamics, particularly those dealing with problems involving the application of Bernoulli's equation and differential equations in real-world scenarios.

Co2
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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
 
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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?
 
Last edited:


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
 


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.
 


got it... thank you so much
 


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

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