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2 years ago

8

Given a two-dimensional steady inviscid air flow field with no body forces described by the velocity field given below. Assuming

the density is constant find the pressure gradient in the x direction at a certain point specified by (x=3, y=2).
u = 2x

v = 3x - 2y

1 answer:

kolbaska11 [484]2 years ago

4 0

Answer:

the pressure gradient in the x direction = -15.48Pa/m

Explanation:

The concept of partial differentiation was used in the determination of the expression for u and v.
each is partially differentiated with respect to x and the appropriate substitution was done to get the value of the pressure gradient as shown in the attached file.

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Fiesta28 [93]

the function is to provide sealed combustion so that the loss of gas is minimized

6 0

1 year ago

An automated transfer line is to be designed. Based on previous experience, the average downtime per occurrence = 5.0 min, and t

IRINA_888 [86]

Answer:

a) 28 stations

b) Rp = 21.43

E = 0.5

Explanation:

Given:

Average downtime per occurrence = 5.0 min

Probability that leads to downtime, d= 0.01

Total work time, Tc = 39.2 min

a) For the optimum number of stations on the line that will maximize production rate.

Maximizing Rp =minimizing Tp

Tp = Tc + Ftd

$= \frac{39.2}{n} + (n * 0.01 * 5.0)$

$= \frac{39.2}{n} + (n * 0.05)$

At minimum pt. = 0, we have:

dTp/dn = 0

$= \frac{-39.2}{n^2} + 0.05 = 0$

Solving for n²:

$n^2 = \frac{39.2}{0.05} = 784$

$n = \sqrt{784} = 28$

The optimum number of stations on the line that will maximize production rate is 28 stations.

b) $Tp = \frac{39.2}{28} + (28 * 0.01 * 5)$

Tp = 1.4 +1.4 = 2.8

The production rate, Rp =

$\frac{60min}{2.8} = 21.43$

The proportion uptime,

$E = \frac{1.4}{2.8} = 0.5$

3 0

2 years ago

The cubic capacity of a four-stroke over-square spark-ignition engine is 245cc. The over-square ratio is (1.1) The clearance vol

pashok25 [27]

Answer:

Bore = 7 cm

stroke = 6.36 cm

compression ratio = 10.007

Explanation:

Given data:

Cubic capacity of the engine, V = 245 cc

Clearance volume, v = 27.2 cc

over square-ratio = 1.1

thus,

D/L = 1.1

where,

D is the bore

L is the stroke

Now,

V = $\frac{\pi}{4}D^2L$

or

V = $\frac{\pi}{4}\frac{D^3}{1.1}$

on substituting the values, we have

245 = $\frac{\pi}{4}\frac{D^3}{1.1}$

or

D = 7.00 cm

Now,

we have

D/L = 1.1

thus,

L = D/1.1

L = 7/1.1

or

L= 6.36 cm

Now,

the compression ratio is given as:

$\textup{compression ratio}=\frac{V+v}{v}$

on substituting the values, we get

$\textup{compression ratio}=\frac{245+27.2}{27.2}$

or

Compression ratio = 10.007

4 0

3 years ago

Determine the speed of sound in air at 400 K. Also determine the Mach number of an aircraft moving in the air at a velocity of 3

Reika [66]

Answer:

$\alpha = \sqrt{1.4 *0.287 \frac{KJ}{Kg K}*\frac{1000J}{1KJ} *400 K}= 400.899 m/s$

$Ma= \frac{310 m/s}{400.899 m/s}= 0.773$

Explanation:

For this case we have given the following data:

$T= 400 K$ represent the temperature for the air

$v = 310 m/s$ represent the velocity of the air

$k = 1.4$ represent the specific heat ratio at the room

$R = 0.287 KJ/ Kg K$ represent the gas constant for the air

And we want to find the velocity of the air under these conditions.

We can calculate the spped of the sound with the Newton-Laplace Equation given by this equation:

$\alpha = \sqrt{\frac{K}{\rho}}=\sqrt{k RT}$

Where K = is the Bulk Modulus of air, k is the adiabatic index of air= 1.4, R = the gas constant for the air, $\rho$ the density of the air and T the temperature in K

So on this case we can replace and we got:

$\alpha = \sqrt{1.4 *0.287 \frac{KJ}{Kg K}*\frac{1000J}{1KJ} *400 K}= 400.899 m/s$

The Mach number by definition is "a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound" and is defined as:

$Ma=\frac{v}{\alpha}$

Where v is the flow velocity and $\alpha$ the volocity of the sound in the medium and if we replace we got:

$Ma= \frac{310 m/s}{400.899 m/s}= 0.773$

And since the Ma<0.8 we can classify the regime as subsonic.

7 0

3 years ago

The convection coefficient for flow over a solid sphere may be determined by submerging the sphere, which is initially at 25 °C,

sashaice [31]

Answer:

t = 59.37 s

Explanation:

Given data:

thermal diffusivity $= \alpha = \frac{k}{\rho c_p} =0.40\times 10^{-0.5}$

theraml conductivity = k = 22 W/m.K

h = 300 W/ m^2.K

$T_i$ = 25 degree C = 298 k

$T_o$ = 60 degree C = 333 k

$T_{\infty}$ = 75 degree C = 348 L

diameter d = 0.1 m

characteristics length Lc = r/3 = = 0.0166

$Bi = \frac{hLc}{K} = \frac{300\times 0.0166}{22} = 0.226$

$\tau = \frac{\alpha t}{lc^2} = \frac{0.4\times 10^{-5}\times t}{0.0166^2}$

$\tau = 0.036 t$

$\frac{T_o -T_{\infty}}{T_i -T_{\infty}} = Ae^[\lambda^2 \tau}$

at Bi = 0.226

Ai = 0.982

$\lambda = 0.876$

$\frac{333348}{298-348} = 0.982e^{-0.879^2 0.036t}$

$0.3 = 0.982 e^{-0.2t}$

$0.305 = e^{-0.2t}$

-1.187 = - 0.02t

t = 59.37 s

7 0

2 years ago