Fluid originally flows through a tube at a rate of 120 cm 3 /s. To illustrate th

Question

Fluid originally flows through a tube at a rate of 120 cm3/s. To illustrate the sensitivity of flow rate to various factors, calculate the new flow rate (in cm3/s) for the following changes with all other factors remaining the same as in the original conditions.

(a) Pressure difference increases by a factor of 1.40.

_________ cm3/s

(b) A new fluid with 3.00 times greater viscosity is substituted.

__________ cm3/s

(c) The tube is replaced by one having 4.00 times the length.

___________ cm3/s

(d) Another tube is used with a radius 0.100 times the original.

__________ cm3/s

(e) Yet another tube is substituted with a radius 0.100 times the original and half the length, and the pressure difference is increased by a factor of 1.50.

___________ cm3/s

Explanation / Answer

a) I hate wording like this.
If the pressure difference INCREASES by a factor of 1.40, then
new flow rate = 120cm³/s * (1 + 1.40) = 288 cm³/s

But they might have INTENDED us to answer
new flow rate = 120cm³/s * 1.40 = 168 cm³/s

(b) 120cm³/s / 3 = 40 cm³/s

(c) 120cm³/s / 3 = 40.0 cm³/s

(d) 120cm³/s * (0.1) = 0.012 cm³/s

(e) 120cm³/s * 2.5 * 1/½ * (0.1) = 0.06 cm³/s
with the same caveat as option (a).

so might have 120cm³/s * 1.5 * 1/½ * (0.1) = 0.036 cm³/s

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