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rjkz [21]
3 years ago
6

A compressed-air drill requires an air supply of 0.25 kg/s at gauge pressure of 650 kPa at the drill. The hose from the air comp

ressor to the drill has a 40 mm diameter and is smooth. The maximum compressor discharge gauge pressure is 690 kPa. Neglect changes in air density and any effects of hose curvature. Air leaves the compressor at 40° C. What is the longest hose that can be used?
Engineering
1 answer:
Klio2033 [76]3 years ago
5 0

Answer:

L = 46.35 m

Explanation:

GIVEN DATA

\dot m  = 0.25 kg/s

D = 40 mm

P_1 = 690 kPa

P_2 = 650 kPa

T_1 = 40° = 313 K

head loss equation

[\frac{P_1}{\rho} +\alpha \frac{v_1^2}{2} +gz_1] -[\frac{P_2}{\rho} +\alpha \frac{v_2^2}{2} +gz_2] = h_l +h_m

whereh_l = \frac{ flv^2}{2D}

h_m minor loss

density is constant

v_1 = v_2

head is same so,z_1 = z_2

curvature is constant so\alpha = constant

neglecting minor losses

\frac{P_1}{\rho}  -\frac{P_2}{\rho} = \frac{ flv^2}{2D}

we know\dot m is given as= \rho VA

\rho =\frac{P_1}{RT_1}

\rho =\frac{690 *10^3}{287*313} = 7.68 kg/m3

therefore

v = \frac{\dot m}{\rho A}

V =\frac{0.25}{7.68 \frac{\pi}{4} *(40*10^{-3})^2}

V = 25.90 m/s

Re = \frac{\rho VD}{\mu}

for T = 40 Degree, \mu = 1.91*10^{-5}

Re =\frac{7.68*25.90*40*10^{-3}}{1.91*10^{-5}}

Re = 4.16*10^5 > 2300 therefore turbulent flow

for Re =4.16*10^5 , f = 0.0134

Therefore

\frac{P_1}{\rho}  -\frac{P_2}{\rho} = \frac{ flv^2}{2D}

L = \frac{(P_1-P_2) 2D}{\rho f v^2}

L =\frac{(690-650)*`10^3* 2*40*10^{-3}}{7.68*0.0134*25.90^2}

L = 46.35 m

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  • let heat capacity rate for cold and hot fluid = C<em>c</em> and C<em>h </em>respectively

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Q<em>max</em> = C<em>min </em>(Inlet Temp. of hot fluid - Inlet Temp. of cold fluid)

Q<em>max</em> = (5.016 kW/°c)(160 - 20) °c

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Q = C<em>min (</em>outlet Temp. of cold fluid - inlet Temp. of cold fluid)

Q = (5.016 kW/°c)(80 - 20) °c

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            .<em>4 Fourth, we determine Effectiveness of the heat exchanger, </em>ε

ε<em> </em>= Q/Qmax

ε <em>= </em>303.66 kW/702.24 kW

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           .<em>5 Fifth, using appropriate  effective relation for double pipe counter flow to determine NTU for the heat exchanger</em>

NTU = \\ \frac{1}{C-1} ln(\frac{ε-1}{εc -1} )

NTU = \frac{1}{0.582-1} ln(\frac{0.432 -1}{0.432 X 0.582   -1} )

NTU = 0.661

          <em>.6 sixth, we determine Heat Exchanger surface area, As</em>

From the question, the overall heat transfer coefficient U = 640 W/m²

As = \frac{NTU C{min} }{U}

As = \frac{0.661 x 5016 W. °c }{640 W/m²}

As = 5.18 m²

            <em>.7 Finally, we determine the length of the heat exchanger, L</em>

L = \frac{As}{\pi D}

L = \frac{5.18 m² }{\pi (0.015 m)}

L= 109.91 m

L ≅ 110 m = 11,000 cm

3 0
3 years ago
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