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QveST [7]
2 years ago
12

A drainage ditch alongside a highway with a 3% grade has a rectangular cross-section of depth 4 ft and width 8 ft, and is fully

packed with fragments of effective diameter of 5 inches. The void fraction within the drainage ditch is 0.42. During a rainstorm, what is the maximum capacity of the drainage ditch in gpm if the water just reaches the top of the ditch?
Engineering
1 answer:
bekas [8.4K]2 years ago
4 0

To solve the problem it is necessary to use the concepts related to frictional dissipation per unit mass, energy balance equation and Volumetric flow rate.

The frictional dissipation per unit mass is defined as

F = \frac{150u_0\mu L(1-\epsilon)^2}{\rho D^2_p\epsilon^3}+1.75\frac{u_0^2L(1-\epsilon)}{D_p\epsilon^3}

Where,

u_0 = Superficial velocity of fluid

\mu = Fluid viscoisty

\epsilon = Porosity

\rho = Fluid density

L = Packed bed length

D_p = Effective particle diameter

Through energy balance equation we have that

\Delta\frac{u^2}{2}+g\Delta z+\frac{\Delta p}{\rho}+w+F=0

Neglect the change in velocity and pressure and the work done we have,

g\Delta z+F = 0

g\Delta z+\frac{150u_0\mu L(1-\epsilon)^2}{\rho D^2_p\epsilon^3}+1.75\frac{u_0^2L(1-\epsilon)}{D_p\epsilon^3}=0

g\frac{\Delta z}{L}+\frac{150u_0\mu (1-\epsilon)^2}{\rho D^2_p\epsilon^3}+1.75\frac{u_0^2(1-\epsilon)}{D_p\epsilon^3}=0

We have also that de grade is defined as

tan\theta = \frac{\Delta z}{L}

tan\theta = 0.03

With our values and replacing at the previous equation we have,

(32.17)(-0.03)+\frac{150u_0(0.000672) (1-0.42)^2}{62.3 (0.417)^2 (0.42)^3}+1.75\frac{u_0^2(1-0.42)}{(0.417)(0.42)^3}=0

32.85u_0^2+0.04225u_0-0.9651=0

u_0 = 0.171ft/s

Previously with the given depth and height we have to

A=4*8

A=32ft^2

Therefore the Volumetric flow rate,

Q=u_0A

Q=(0.171ft/s)(32ft^2)(60s/1min)(1gal/0.133681ft^3)

Q= 2456gal/min

Therefore the desired volumetric flow rate is 2456gal/min

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3–102 One of the common procedures in fitness programs is to determine the fat-to-muscle ratio of the body. This is based on the
gayaneshka [121]

Answer:

x_fat = [ 0.5*(Wsa + Wsw) -  p_muscle*V ] / V*( p_fat - p_muscle )

Explanation:

Given:

- The total volume of body = V

- The average density of the body = p_avg

- The density of muscle = p_muscle

- The density of fat = p_fat

Find:

Obtain a relation for the volume fraction of body fat x_fat

Solution:

- The volume of the fat is given by:

                          V_fat = x_fat*V

- The volume of the muscle is given by:

                          V_muscle = V - V_fat

                                            = V - x_fat*V

                                            =V*( 1 - x_fat )

- We will use the conservation of mass for the body related as:

                         mass_fat + mass_muscle = Total average mass

                         p_fat*V_fat + p_muscle*V_muscle = p_avg*V

                         p_fat*x_fat*V + p_muscle*V*( 1 - x_fat ) = p_avg*V

                         p_fat*x_fat + p_muscle*( 1 - x_fat ) = p_avg

- To determine p_1 we weigh the body in air:

                         Weight reading (Wsa) = m = p_1*V

                         p_1 = Wsa / V*g

- To determine p_2 we weigh the body in water:

                         Weight reading (Wsw) = m - p_w*V= p_1*V - p_w*V

                         Weight reading (Wsw) = V*(p_1 - p_w) = V*(p_2)

                         Where, p_2 = p_1 - p_water

                         p_2 = Wsw / V

- The average density p_avg:

                         p_avg = 0.5*(p_1 + p_2)  

                         p_avg = 0.5*(Wsa / V + Wsw / V)  

                         p_avg = 0.5*(Wsa + Wsw) / V                      

- Plug in the mass equation:

                         p_fat*x_fat + p_muscle*( 1 - x_fat ) = 0.5*(Wsa + Wsw) / V

                         x_fat*( p_fat - p_muscle ) = 0.5*(Wsa + Wsw) / V - p_muscle

                   x_fat = [ 0.5*(Wsa + Wsw) -  p_muscle*V ] / V*( p_fat - p_muscle )

                         

6 0
3 years ago
A charge of +2.00 μC is at the origin and a charge of –3.00 μC is on the y axis at y = 40.0 cm . (a) What is the potential at po
Nimfa-mama [501]

a) Potential in A: -2700 V

b) Potential difference: -26,800 V

c) Work: 4.3\cdot 10^{-15} J

Explanation:

a)

The electric potential at a distance r from a single-point charge is given by:

V(r)=\frac{kq}{r}

where

k=8.99\cdot 10^9 Nm^{-2}C^{-2} is the Coulomb's constant

q is the charge

r is the distance from the charge

In this problem, we have a system of two charges, so the total potential at a certain point will be given by the algebraic sum of the two potentials.

Charge 1 is

q_1=+2.00\mu C=+2.00\cdot 10^{-6}C

and is located at the origin (x=0, y=0)

Charge 2 is

q_2=-3.00 \mu C=-3.00\cdot 10^{-6}C

and is located at (x=0, y = 0.40 m)

Point A is located at (x = 0.40 m, y = 0)

The distance of point A from charge 1 is

r_{1A}=0.40 m

So the potential due to charge 2 is

V_1=\frac{(8.99\cdot 10^9)(+2.00\cdot 10^{-6})}{0.40}=+4.50\cdot 10^4 V

The distance of point A from charge 2 is

r_{2A}=\sqrt{0.40^2+0.40^2}=0.566 m

So the potential due to charge 1 is

V_2=\frac{(8.99\cdot 10^9)(-3.00\cdot 10^{-6})}{0.566}=-4.77\cdot 10^4 V

Therefore, the net potential at point A is

V_A=V_1+V_2=+4.50\cdot 10^4 - 4.77\cdot 10^4=-2700 V

b)

Here we have to calculate the net potential at point B, located at

(x = 0.40 m, y = 0.30 m)

The distance of charge 1 from point B is

r_{1B}=\sqrt{(0.40)^2+(0.30)^2}=0.50 m

So the potential due to charge 1 at point B is

V_1=\frac{(8.99\cdot 10^9)(+2.00\cdot 10^{-6})}{0.50}=+3.60\cdot 10^4 V

The distance of charge 2 from point B is

r_{2B}=\sqrt{(0.40)^2+(0.40-0.30)^2}=0.412 m

So the potential due to charge 2 at point B is

V_2=\frac{(8.99\cdot 10^9)(-3.00\cdot 10^{-6})}{0.412}=-6.55\cdot 10^4 V

Therefore, the net potential at point B is

V_B=V_1+V_2=+3.60\cdot 10^4 -6.55\cdot 10^4 = -29,500 V

So the potential difference is

V_B-V_A=-29,500 V-(-2700 V)=-26,800 V

c)

The work required to move a charged particle across a potential difference is equal to its change of electric potential energy, and it is given by

W=q\Delta V

where

q is the charge of the particle

\Delta V is the potential difference

In this problem, we have:

q=-1.6\cdot 10^{-19}C is the charge of the electron

\Delta V=-26,800 V is the potential difference

Therefore, the work required on the electron is

W=(-1.6\cdot 10^{-19})(-26,800)=4.3\cdot 10^{-15} J

4 0
3 years ago
It is appropriate to use the following yield or failure criterion for ductile materials (a) Maximum shear stress or Tresca crite
Nataly [62]

Answer:

(b)Distortion energy theory.

Explanation:

The best suitable theory for ductile material:

       (1)Maximum shear stress theory (Guest and Tresca theory)

It theory state that applied maximum shear stress should be less or equal to its maximum shear strength.

      (2)Maximum distortion energy theory(Von Mises henkey's        theory)

It states that maximum shear train energy per unit volume at any point  is equal to strain energy per unit volume under the state of uni axial stress condition.

But from these two Best theories ,suitable theory is distortion energy theory ,because it gives best suitable result for ductile material.

6 0
2 years ago
Given a matrix, clockwise-rotate elements in it. Please add code to problem3.cpp and the makefile. Use the code in p3 to test yo
rusak2 [61]

Answer:

/* C Program to rotate matrix by 90 degrees */

#include<stdio.h>

int main()

{

int matrix[100][100];

int m,n,i,j;

printf("Enter row and columns of matrix: ");

scanf("%d%d",&m,&n);

 

/* Enter m*n array elements */

printf("Enter matrix elements: \n");

for(i=0;i<m;i++)

{

 for(j=0;j<n;j++)

 {

  scanf("%d",&matrix[i][j]);

 }

}

 

/* matrix after the 90 degrees rotation */

printf("Matrix after 90 degrees roration \n");

for(i=0;i<n;i++)

{

 for(j=m-1;j>=0;j--)

 {

  printf("%d  ",matrix[j][i]);

 }

 printf("\n");

}

 

return 0;

 

}

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