3. Consider a vortex filament of strength in the shape of a closed circular loop of radius R. Obtain an expression for the vel
ocity induced at the center of the loop in terms of and R, no other variables. Tip: Draw the loop on your page. If the vortices on the filament curve inward over the top of the loop, then the velocity vector points into the page, and vice-versa. Draw your vectors (dl and r) clearly to ensure you get the sign of the velocity vector correct. Your result will be a vector
1 answer:
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Answer:
Explanation:
The question can be well structured in a table format as illustrated below:
Tensile Strength (MPa) Number- Average Molecular Weight (g/mol)
82 12,700
156 28,500
The tensile strength and number-average molecular weight for two polyethylene materials given above.
Estimate the number-average molecular weight that is required to give a tensile strength required above. Using the data given find TS (infinity) in MPa.
<u>SOLUTION:</u>
We know that :
where;
= Tensile Strength
= Tensile Strength (Infinity)
= Number- Average Molecular Weight (g/mol)
SO;
From equation (1) ; collecting the like terms; we have :
From equation (2) ; we have:
So;
Then;
Solving by L.C.M
By cross multiplying ; we have:
Collecting like terms ; we have
Dividing both sides by 15800:
A = 1695208.861
From equation (1);
Replacing A = 1695208.861 in the above equation; we have:
From equation(2);
Replacing A = 1695208.861 in the above equation; we have:
We are to also estimate the number- average molecular weight that is required to give a tensile strength required above.
If the Tensile Strength (MPa) is 82 MPa
Definitely the average molecular weight will be = 12,700 g/mol
If the Tensile Strength (MPa) is 156 MPa
Definitely the average molecular weight will be = 28,500 g/mol
But;
Let us assume that the Tensile Strength (MPa) = 181 MPa for example.
Using the same formula:
Then:
Collecting like terms ; we have:
1695208.861= 34.481
Dividing both sides by 34.481; we have:
=
Answer:
(i) 169.68 volt
(ii) 16.90 volt
(iii) 16.90 volt
(iv) 108.07 volt
(v) 2.161 A
Explanation:
Turn ratio is given as 10:1
We have given that input voltage
(i) We know that peak voltage is give by
(ii) We know that for transformer
So
So peak voltage in secondary will be 16.90 volt
(iii) Peak voltage of the rectifier will be equal to the peak voltage of the secondary
So peak voltage of the rectifier will be 16.90 volt
(iv) Dc voltage of the rectifier is given by
(v) Now dc current is given by