Poiseuille's Law gives the rate of flow, R, of a gas through a cylindrical pipe in terms of the radius of the pipe, r, for a fixed drop in pressure between the two ends of the pipe.

(a) Find a formula for Poiseuille's Law, given that the rate of flow is proportional to the fourth power of the radius. Use k for the proportionality constant. R(r) =--

(b) If R = 400 cm3/sec in a pipe of radius 4 cm for a certain gas, find a formula for the rate of flow of that gas through a pipe of radius r. R(r) = -

(c) What is the rate of flow of the same gas through a pipe of radius 3?

a) R(r) = kr⁴

b) R(r) = 1.5625 r⁴

c) R = 126.56 cm³/s when r = 3 cm

Step-by-step explanation:

Rate of flow of a gas through a cylindrical pipe = R

radius of the pipe = r

a) R ∝r⁴

R(r) = kr⁴ where k is the proportionality constant.

R(r) means R is a function of r.

b) R(r) = kr⁴

R = 400 cm³/s, r = 4 cm

400 = k × 4⁴

k = 400/4⁴ = 400/256 = 1.5625 (cm.s)⁻¹

R(r) = 1.5625 r⁴

c) R(r) = 1.5625 r⁴

R = ?

r = 3 cm

R = 1.5625 × 3⁴ = 126.5625 cm³/s = 126.56 cm³/s

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!

i only know the sequence of arithmetic it adds the first is 5+4 then it goes up as it adds to then it is 9+5 then 14+6 then to 20+7 and so on. 5,9,14,20,27,35.

step-by-step explanation: