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:Problem with a cylinder tank and a nozzle

  1. Apr 17, 2012 #1

    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
     
    Last edited by a moderator: Apr 17, 2012
  2. jcsd
  3. Apr 17, 2012 #2
    Re: urgent :Problem with a cylinder tank and a nozzle

    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: Apr 17, 2012
  4. Apr 17, 2012 #3

    Co2

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    Re: urgent :Problem with a cylinder tank and a nozzle

    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
     
  5. Apr 17, 2012 #4
    Re: urgent :Problem with a cylinder tank and a nozzle

    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.
     
  6. Apr 17, 2012 #5

    Co2

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    Re: urgent :Problem with a cylinder tank and a nozzle

    got it... thank you so much
     
  7. Apr 19, 2012 #6
    Re: urgent :Problem with a cylinder tank and a nozzle

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