Fluid originally flows through a tube at a rate of 100 cm3 /s . To illustrate the sensitivity of flow rate to various factors, calculate the new flow rate for the following changes with all other factors remaining the same as in the original conditions. (a) Pressure difference increases by a factor of 1.50. (b) A new fluid with 3.00 times greater viscosity is substituted. (c) The tube is replaced by one having 4.00 times the length. (d) Another tube is used with a radius 0.100 times the original. (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.

Solution 34PE

Step 1 of 7

In the given case, we need to calculate the new flow rate through a tube if the fluid initially flowing at rate , when the following changes are made keeping all other factors same as in the initial case.

Given data,

Original flow rate,

To find,

- New flow rate, when pressure difference increase by a factor of 1.50,
- New flow rate, when a new fluid with 3 times greater viscosity is used,
- New flow rate, when the original tube is replaced by 4 times of its length,
- New flow rate, when the original tube is replaced by a new tube with radius 0.1 times the original,
- New flow rate, when the original tube is replaced by a new tube with radius 0.1 times the original and half the original length, also the pressure difference is increased by 1.5 times,