Answer:
a) R = Kr⁴
b) R = (500/256) r⁴ = (125/64) r⁴ = 1.953125 r⁴
c) R = 1220.7 cm³/s
Step-by-step explanation:
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) R ∝ r⁴
R = Kr⁴
Note that all the other parameters that are constant like the fixed pressure drop between the ends of the pipe are all represented by the constant of proportionality, K.
b) If R= 500 cm^3/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 cm. Enter the exact answer.
R = Kr⁴
R = 500 cm³/s
r = 4 cm
500 = K × 4⁴
K = (500/256)
K = 1.953125
R = Kr⁴ becomes
R = 1.953125 r⁴
c) The rate of flow of the gas in part (b) through a pipe with a 5 cm radius.
R = 1.953125 r⁴
r = 5 cm
R = 1.953125 (5⁴)
R = 1,220.703125 = 1220.7 cm³/s
Hope this Helps!!!
This is a conversion problem (meters to nanometers) so all you do is use the values given to you in the question.
We know that 1 meter = 1*10^9 nanometers, meaning that for every one meter is also 1*10^9 nanometers and vice versa. So we can set up the "train tracks"
[
tex] \frac{1*10^9 nanometers}{1 meter} * (1*10^-5 meters) [/tex]
I set it up that way because it cancels out the units "meters" since 1 meter is in the denominator and the other meter is in the numerator.
Then I'll be left with:
Now we can solve as is.
From the Figure We can Notice that :
Opposite Side - AB = 1
Adjacent Side - OB =
We know that :
⇒ θ = 30°
We know that :
⇒
⇒
⇒ AO = 2
Answer:
22.75 minutes or 22 minutes 45 seconds
Step-by-step explanation:
Okay, this is a working together question. Let’s walk through it together!
Firstly, let’s say the total volume of the swimming pool is x sq.meters
Now, the rate of the smaller hose would be x/65 while that of the larger will be x/35
Now, their combined rate would be x/65 + x/35 = 100x/2275
Now, since the volume is x, the time taken is simply, the volume divided by the joint rate. That is mathematically equal to x divided by 100x/2275
x * 2275/100x = 2275/100 = 22.75 minutes or 22 minutes 45 seconds
Answer:
D)
Step-by-step explanation:
You have to use the laws of exponents to solve this:
Power of a Power: . In this case, , all of the numbers in the parenthesis need to be multiplied to the power of 3: .
Quotient of Powers: . In this case, , all of the exponents need to be subtracted (but the 4³ (64) and 8 need to be divided): .
Use the Power of a Power again for the expression at the right: . You get: . Keep the subtraction/negative sign where it is.
Together, you get: .
Hope it helps!