Question

A manufacturer makes two types of drinking straws: one with a square cross-sectional shape, and the other type the typical round shape. The amount of material in each straw is to be the same. That is, the length of the perimeter of the cross section of each shape is the same. For a given pressure drop, what is the ratio of the flowrates through the straws?

Answer 1

Answer:

$\frac{Q_{square}}{Q_{circle}} = 0.785$  

Explanation:

given data

types of drinking straws

1. square cross-sectional shape
2. round shape

solution

we know that both perimeter of the cross section are equal

so we can say that

perimeter of square  = perimeter of circle  

4 × S = π × D

here S is length and D is diameter

S = $\frac{\pi D}{4}$        ....................1

and

ratio of  flow rate through the square and circle is here

$\frac{Q_{square}}{Q_{circle}} = \frac{AV^2}{AV^2}$  

$\frac{Q_{square}}{Q_{circle}} = \frac{S^2}{\frac{\pi D^2}{4}}$  

$\frac{Q_{square}}{Q_{circle}} = \frac{(\frac{\pi D}{4})^2}{\frac{\pi D^2}{4}}$  

$\frac{Q_{square}}{Q_{circle}} = \frac{\pi }{4}$  

$\frac{Q_{square}}{Q_{circle}} = 0.785$