Question

The pressure in a 150-cm diameter pipe 2,000 m long is 30 N/cm2. Determine the amount of water that will enter the pipe if the pressure increases to 30 bars. Assume the pipe is rigid and does not increase its volume.

Answer 1

Answer:

The flow rate is 9 times of initial flow rate.

Explanation:

Given that,

Pressure P= 30 N/cm²

Increases pressure P'=30 bars

We need to calculate the amount of water

Using formula of volume flow rate

$Q=\dfrac{\pi\Delta P D^4}{128\mu L}$

D and L remain same

So, $\dfrac{Q_{2}}{Q_{1}}=\dfrac{\Delta P_{2}}{\Delta P_{1}}$

Put the value into the formula

$\dfrac{Q_{2}}{Q_{1}}=\dfrac{30\times10^{5}}{30\times10^{4}}$

$\dfrac{Q_{2}}{Q_{1}}=10$

$Q_{2}=10Q_{1}$

We need to calculate the change in flow rate

$\Delta Q=Q_{2}-Q_{1}$

$\Delta Q=10Q_{1}-Q_{1}$

$\Delta Q=9Q_{1}$

Hence, The flow rate is 9 times of initial flow rate.