If all other conditions (ie Pressure differential, orientation of gravity) and dimensions are unchanged, what is the effect of doubling the cylinder diameter on the volume flow rate? A. The flow rate decreases by a factor of 4 B. The flow rate decreases by a factor of 1.189 C. The flow rate doubles D. The flow rate increases by a factor of 16
Question
If all other conditions (ie Pressure differential, orientation of gravity) and dimensions are unchanged, what is the effect of doubling the cylinder diameter on the volume flow rate? A. The flow rate decreases by a factor of 4 B. The flow rate decreases by a factor of 1.189 C. The flow rate doubles D. The flow rate increases by a factor of 16
Solution
The volume flow rate in a cylinder is given by the equation Q=πr²v, where r is the radius of the cylinder and v is the velocity of the fluid. If the diameter of the cylinder is doubled, the radius is also doubled. Substituting this into the equation gives Q=π(2r)²v=4πr²v. This means that the volume flow rate quadruples, or increases by a factor of 4. Therefore, none of the options A, B, C, D are correct.
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