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3.25: Untitled Page 51

  • Page ID
    18184
  • Chapter 3

    Figure 3.11b. Angle, (

    t) for draining the system illustrated in Figure 3.11a.

    Figure 3.11c. Angle, (

    t) for filling the system illustrated in Figure 3.11a.

    The length and radius of the tank under consideration are given by L  8 ft ,

    R  1 5

    . ft

    (6)

    index-96_1.png

    index-96_2.png

    Single component systems

    87

    Part IIIa. Given the conditions, Q   0 4

    . 5 gal/min and   0 when t  0 , use Figure 3.11b to determine the time required to completely drain the tank.

    Part IIIb. If the initial depth of the tank is h  0 . 6 ft and the net flow into the tank is Q  0 5

    . 5 gal/min , use Figure 3.11c to determine the time required to fill the tank. While Figure 3.11c has been constructed on the basis that   2 when t  0 , a little thought will indicate that it can be used for other initial conditions.

    3‐12. A cylindrical tank of diameter D is filled to a depth as illustrated in

    o

    h

    Figure 3.12. At t  0 a plug is pulled from the bottom of the tank and the Figure 3.12. Draining tank

    volumetric flow rate through the orifice is given by what is sometimes known as Torricelli’s law (Rouse and Ince, 1957)

    Q C A

     

    o

    2

    d

    p

    (1)

    Here C is a discharge coefficient having a value of 0.6 and d

    o

    A is the area of the

    orifice. If the cross‐sectional area of the tank is large compared to the area of the orifice, the pressure in the tank is essentially hydrostatic and  p is given by

    p   g h

    (2)

    index-97_1.png

    index-97_2.png

    index-97_3.png

    88