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patriot [66]
3 years ago
7

A steady state and continuous separator has a total feed rate of 100. kg/h of a 55.0 wt. % benzene mixture. The balance is tolue

ne (i.e., 45 wt. % toluene). A vapor stream leaves the process and has a benzene concentration of 85.0% by mass and a liquid stream leaving the process has a benzene concentration of 10.6% by mass. a. Draw and label the process flow chart. Develop a consistent variable naming system. b. Simplify the general balance equation. c. Write and solve the total mass balance and the benzene mass balance.

Engineering
1 answer:
Tju [1.3M]3 years ago
7 0

Answer:

Part a : The flow chart is as given in the attached file

Part b: Overall Mass balance is given as  m_1=m_2+m_3

Part c:  The mass flow rate of Vapor and Liquid are 59.667 kg/hr

and 40.323 kg/hr respectively.

Explanation:

Part a

The flow chart is as given in the attached file.

The labeling is as

Feed Rate  is given as m_1 which is 100 kg/h

Vapour Rate is given as m_2 which is not known

Liquid  Rate is given as m_3 which is not known

Fraction of Benzene at Feed is given as x_1B which is 55% wt.

Fraction of Toluene at Feed is given as x_1T which is 45% wt.

Fraction of Benzene at Vapour is given as x_2B which is 85% wt.

Fraction of Toluene at Vapour is given as x_2T which is 15% wt.

Fraction of Benzene at Liquid is given as x_3B which is 10.6% wt.

Part b

Overall Mass balance is given as

Total Mass in=Total Mass out

m_1=m_2+m_3

100=m_2+m_3               -----------------1

Part c

Benzene Mass Balance is given as

Mass of Benzene in Feed=Mass of Benzene in Vapor+Mass of Benzene in Liquid

x_1B *m1=x_2B*m2+x_3B*m3

0.55*m1=0.85*m2+0.106*m3                    -----------------------2

Solving the 2 equations simultaneously gives

m_2=59.667 kg/hr

m_3=40.323 kg/hr

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Five bolts are used in the connection between the axial member and the support. The ultimate shear strength of the bolts is 320
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Answer:

The minimum allowable bolt diameter required to support an applied load of P = 450 kN is 45.7 milimeters.

Explanation:

The complete statement of this question is "Five bolts are used in the connection between the axial member and the support. The ultimate shear strength of the bolts is 320 MPa, and a factor of safety of 4.2 is required with respect to fracture. Determine the minimum allowable bolt diameter required to support an applied load of P = 450 kN"

Each bolt is subjected to shear forces. In this case, safety factor is the ratio of the ultimate shear strength to maximum allowable shear stress. That is to say:

n = \frac{S_{uts}}{\tau_{max}}

Where:

n - Safety factor, dimensionless.

S_{uts} - Ultimate shear strength, measured in pascals.

\tau_{max} - Maximum allowable shear stress, measured in pascals.

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\tau_{max} = \frac{S_{uts}}{n}

\tau_{max} = \frac{320\times 10^{6}\,Pa}{4.2}

\tau_{max} = 76.190\times 10^{6}\,Pa

Since each bolt has a circular cross section area and assuming the shear stress is not distributed uniformly, shear stress is calculated by:

\tau_{max} = \frac{4}{3} \cdot \frac{V}{A}

Where:

\tau_{max} - Maximum allowable shear stress, measured in pascals.

V - Shear force, measured in kilonewtons.

A - Cross section area, measured in square meters.

As connection consist on five bolts, shear force is equal to a fifth of the applied load. That is:

V = \frac{P}{5}

V = \frac{450\,kN}{5}

V = 90\,kN

The minimum allowable cross section area is cleared in the shearing stress equation:

A = \frac{4}{3}\cdot \frac{V}{\tau_{max}}

If V = 90\,kN and \tau_{max} = 76.190\times 10^{3}\,kPa, the minimum allowable cross section area is:

A = \frac{4}{3} \cdot \frac{90\,kN}{76.190\times 10^{3}\,kPa}

A = 1.640\times 10^{-3}\,m^{2}

The minimum allowable cross section area can be determined in terms of minimum allowable bolt diameter by means of this expression:

A = \frac{\pi}{4}\cdot D^{2}

The diameter is now cleared and computed:

D = \sqrt{\frac{4}{\pi}\cdot A}

D =\sqrt{\frac{4}{\pi}\cdot (1.640\times 10^{-3}\,m^{2})

D = 0.0457\,m

D = 45.7\,mm

The minimum allowable bolt diameter required to support an applied load of P = 450 kN is 45.7 milimeters.

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