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ASHA 777 [7]
3 years ago
8

The cross-section of a rough, rectangular, concrete() channel measures . The channel slope is 0.02ft/ft. Using the Darcy-Weisbac

h friction method, determine the maximum allowable flow rate through the channel to maintain one foot of free board(freeboard is the vertical distance form the water surface to the overtopping level of the channel). For these conditions, find the following characteristics(note that FlowMaster may not directly report all of these):
a) Flow area
b) Wetted perimeter
c) Hydraulic radius(A/P) :
d) Velocity
e) Froude number

Engineering
1 answer:
bazaltina [42]3 years ago
4 0

Answer:

The following are the answer to this question:

Explanation:

In point a, Calculating the are of flow:

\bold{Area =B \times D_f}

         =6\times 5\\\\=30 \ ft^2

In point b, Calculating the wetter perimeter.

\bold{P_w =B+2\times D_f}

      = 6 +2\times (5)\\\\= 6 +10 \\\\=16 \ ft

In point c, Calculating the hydraulic radius:

\bold{R=\frac{A}{P_w}}

   =\frac{30}{16}\\\\= 1.875 \ ft

In point d, Calculating the value of Reynolds's number.

\bold{Re =\frac{4VR}{v}}

     =\frac{4V \times 1.875}{1 \times 10^{-5} \frac{ft^2}{s}}\\\\

     =750,000 V

Calculating the velocity:

V= \sqrt{\frac{8gRS}{f}}

   = \sqrt{\frac{8\times 32.2 \times 1.875 \times 0.02}{f}}\\\\=\frac{3.108}{\sqrt{f}}\\\\

\sqrt{f}=\frac{3.108}{V}\\\\

calculating the Cole-brook-White value:

\frac{1}{\sqrt{f}}= -2 \log (\frac{K}{12 R} +\frac{2.51}{R_e \sqrt{f}})\\\\ \frac{1}{\frac{3.108}{V}}= -2 \log (\frac{2 \times 10^{-2}}{12 \times 1.875} +\frac{2.51}{750,000V\sqrt{f}})\\

\frac{V}{3.108} =-2\log(8.88 \times 10^{-5} + \frac{3.346 \times 10^{-6}}{750,000(3.108)})

After calculating the value of V it will give:

V= 25.18 \ \frac{ft}{s^2}\\

In point a, Calculating the value of Froude:

F= \frac{V}{\sqrt{gD}}

= \frac{V}{\sqrt{g\frac{A}{\text{Width flow}}}}\\

= \frac{25.18}{\sqrt{32.2\frac{30}{6}}}\\\\= \frac{25.18}{\sqrt{32.2 \times 5}}\\\\= \frac{25.18}{\sqrt{161}}\\\\=  \frac{25.18}{12.68}\\\\= 1.98

The flow is supercritical because the amount of Froude is greater than 1.  

Calculating the channel flow rate.

Q= AV

   =30x 25.18\\\\= 755.4 \ \frac{ft^3}{s}\\

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Answer:

Part a: The volume of vessel is 4.7680m^3 and total internal energy is 3680 kJ.

Part b: The quality of the mixture is 90.3%  or 0.903, temperature is 120 °C and total internal energy is 4660 kJ.

Explanation:

Part a:

As per given data

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Specific volume of saturated liquid=v_f=0.00102 m^3/kg

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v=\frac{V}{m}\\V=v \times m\\V=2.38399 \times 2\\V=4.7680 m^3

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Similarly for T=80 and dryness ratio of 0.7 from the table of steam

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Specific internal energy is given as u=1840 kJ/kg

So the total internal energy is given as

u=\frac{U}{m}\\U=u \times m\\U=1840 \times 2\\U=3680 kJ

The total internal energy is 3680 kJ.

So the volume of vessel is 4.7680m^3 and total internal energy is 3680 kJ.

Part b

Volume of vessel is given as 1.6

mass is given as 2 kg

Pressure is given as 0.2 MPa or 200 kPa

Now the specific volume is given as

v=\frac{V}{m}\\v=\frac{1.6}{2}\\v=0.8 m^3/kg

So from steam tables for Pressure=200 kPa and specific volume as 0.8 gives

Temperature=T=120 °C

Quality=x=0.903 ≈ 90.3%

Specific internal energy =u=2330 kJ/kg

The total internal energy is given as

u=\frac{U}{m}\\U=u \times m\\U=2330 \times 2\\U=4660 kJ

So the quality of the mixture is 90.3%  or 0.903, temperature is 120 °C and total internal energy is 4660 kJ.

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