Ask question

Ask question

All categories

3 years ago

12

Consider steady, incompressible, laminar flow of a Newtonian fluid in an infinitely long round pipe annulus of inner radius Ri a

nd outer radius Ro Ignore the effects of gravity. A constant negative pressure gradient _P/_x is applied in the x-direction, (∂P/∂x)=(P1-P2)/(x2-x1) where x1 and x2 are two arbitrary locations along the x-axis, and P1 and P2 are the pressures at those two locations. The pressure gradient may be caused by a pump and/or gravity. Note that we adopt a modified cylindricaloordinate system here with x instead of z for the axial component, namely, ( r, θ ,x) and (Ur, Uθ ,Ux) Derive an expression for the velocity field in the annular space in the pipe.

1 answer:

svetlana [45]3 years ago

8 0

Answer:

is it multiple choice?

Explanation:

You might be interested in

A vertical cylinder (Fig. P3.227) has a 61.18-kg piston locked with a pin, trapping 10 L of R-410a at 10◦C with 90% quality insi

Whitepunk [10]

Hey! How are you? My name is Maria, 19 years old. Yesterday broke up with a guy, looking for casual sex.

Write me here and I will give you my phone number - *pofsex.com*

My nickname - Lovely

4 0

2 years ago

The state of plane strain on an element is:

balu736 [363]

Answer:

a. ε₁=-0.000317

ε₂=0.000017

θ₁= -13.28° and θ₂=76.72°

b. maximum in-plane shear strain =3.335 *10^-4

Associated average normal strain ε(avg) =150 *10^-6

θ = 31.71 or -58.29

Explanation:

$\epsilon _{1,2} =\frac{\epsilon_x + \epsilon_y}{2} \pm \sqrt{(\frac{\epsilon_x + \epsilon_y}{2} )^2 + (\frac{\gamma_xy}{2})^2} \\\\\epsilon _{1,2} =\frac{-300 \times 10^{-6} + 0}{2} \pm \sqrt{(\frac{-300 \times 10^{-6}+ 0}{2}) ^2 + (\frac{150 \times 10^-6}{2})^2}\\\\\epsilon _{1,2} = -150 \times 10^{-6} \pm 1.67 \times 10^{-4}$

ε₁=-0.000317

ε₂=0.000017

To determine the orientation of ε₁ and ε₂

$tan 2 \theta_p = \frac{\gamma_xy}{\epsilon_x - \epsilon_y} \\\\tan 2 \theta_p = \frac{150 \times 10^{-6}}{-300 \times 10^{-6}-\ 0}\\\\tan 2 \theta_p = -0.5$

θ= -13.28° and 76.72°

To determine the direction of ε₁ and ε₂

$\epsilon _{x' }=\frac{\epsilon_x + \epsilon_y}{2} + \frac{\epsilon_x -\epsilon_y}{2} cos2\theta + \frac{\gamma_xy}{2}sin2\theta \\\\\epsilon _{x'} =\frac{-300 \times 10^{-6}+ \ 0}{2} + \frac{-300 \times 10^{-6} -\ 0}{2} cos(-26.56) + \frac{150 \times 10^{-6}}{2}sin(-26.56)\\\\$

=-0.000284 -0.0000335 = -0.000317 =ε₁

Therefore θ₁= -13.28° and θ₂=76.72°

b. maximum in-plane shear strain

$\gamma_{max \ in \ plane} =2\sqrt{(\frac{\epsilon_x + \epsilon_y}{2} )^2 + (\frac{\gamma_xy}{2})^2} \\\\\gamma_{max \ in \ plane} = 2\sqrt{(\frac{-300 *10^{-6} + 0}{2} )^2 + (\frac{150 *10^{-6}}{2})^2}$

=3.335 *10^-4

$\epsilon_{avg} =(\frac{\epsilon_x + \epsilon_y}{2} )$

ε(avg) =150 *10^-6

orientation of γmax

$tan 2 \theta_s = \frac{-(\epsilon_x - \epsilon_y)}{\gamma_xy} \\\\tan 2 \theta_s = \frac{-(-300*10^{-6} - 0)}{150*10^{-6}}$

θ = 31.71 or -58.29

To determine the direction of γmax

$\gamma _{x'y' }= - \frac{\epsilon_x -\epsilon_y}{2} sin2\theta + \frac{\gamma_xy}{2}cos2\theta \\\\\gamma _{x'y' }= - \frac{-300*10^{-6} - \ 0}{2} sin(63.42) + \frac{150*10^{-6}}{2}cos(63.42)$

= 1.67 *10^-4

4 0

3 years ago

La probabilidad de que un nuevo producto tenga éxito es de 0.85. Si se eligen 10 personas al azar y se les pregunta si compraría

liq [111]

Answer:

La probabilidad pedida es $0.820196$

Explanation:

Sabemos que la probabilidad de que un nuevo producto tenga éxito es de 0.85. Sabemos también que se eligen 10 personas al azar y se les pregunta si comprarían el nuevo producto. Para responder a la pregunta, primero definiremos la siguiente variable aleatoria :

$X:$ '' Número de personas que adquirirán el nuevo producto de 10 personas a las que se les preguntó ''

Ahora bien, si suponemos que la probabilidad de que el nuevo producto tenga éxito se mantiene constante $(p=0.85)$ y además suponemos que hay independencia entre cada una de las personas al azar a las que se les preguntó ⇒ Podemos modelar a $X$ como una variable aleatoria Binomial. Esto se escribe :

$X$ ~ $Bi(n,p)$ en donde $''n''$ es el número de personas entrevistadas y $''p''$ es la probabilidad de éxito (una persona adquiriendo el producto) en cada caso.

Utilizando los datos ⇒ $X$ ~ $Bi(10,0.85)$

La función de probabilidad de la variable aleatoria binomial es :

$p_{X}(x)=P(X=x)=\left(\begin{array}{c}n&x\end{array}\right)p^{x}(1-p)^{n-x}$ con $x=0,1,2,...,n$

Si reemplazamos los datos de la pregunta en la función de probabilidad obtenemos :

$P(X=x)=\left(\begin{array}{c}10&x\end{array}\right)(0.85)^{x}(0.15)^{10-x}$ con $x=0,1,2,...,10$

Nos piden la probabilidad de que por lo menos 8 personas adquieran el nuevo producto, esto es :

$P(X\geq 8)=P(X=8)+P(X=9)+P(X=10)$

Calculando $P(X=8), P(X=9)$ y $P(X=10)$ por separado y sumando, obtenemos que $P(X\geq 8)=0.820196$

7 0

3 years ago

I have to find the critical points of this function of two variables <img src="https://tex.z-dn.net/?f=%5C%5Cf%28x%2Cy%29%3Dx%5E

liraira [26]

Answer:

no i dont think there is

Explanation:

because theres not

4 0

3 years ago

Which of the following is true about modern hydraulic lifts?

kaheart [24]

The modern hydraulic lifts make use of biodegradable fluid to transmit hydraulic power

<em>Question: The options are left out in the question. The details and facts about the modern hydraulic lift are presented here</em>

<em />

Details about the modern hydraulic lifts include;

The development of the modern hydraulic occurred in the Industrial Revolution to perform task done previously by steam powered elevators

The power of the hydraulic lift come from the hydraulic cylinder known as the actuator, which in turn is powered by pressurized hydraulic fluid such as oil

The hydraulic fluid is pushed by a piston rod through which energy is capable of being transferred, such that the applied force is multiplied, to provide more power for lifting

<u>Facts about the modern hydraulic lifts include;</u>

The dry motor in the modern hydraulic lift is more efficient and consumes 20% less energy

It comprises of valves that are controlled electronically such that the response is much rapid and the energy consumption is reduced by a further 20%

The cars used in the modern lift are lighter, as well as the slings, which reduces the power usage by 20%

It makes use of chemicals which are environmentally friendly as hydraulic fluid

The flash point of the fluid used is higher, as well as it posses 50% lower compressibility as well elasticity

Learn more here:

brainly.com/question/16942803

6 0

2 years ago