Question

A fire hose has an inside diameter of 6.40 cm. Suppose such a hose carries a flow of 40.0 L/s starting at a gauge pressure of 1.62 x 106 N/m2. Calculate the Reynolds numbers for flow in the fire hose.

Answer 1

Answer:

The Reynolds numbers for flow in the fire hose.

Explanation:

Given that,

Diameter = 6.40 cm

Rate of flow = 40.0 L/s

Pressure $P=1.62\times10^{6}\ N/m^2$

We need to calculate the Reynolds numbers for flow in the fire hose

Using formula of rate of flow

$Q=Av$

$v=\dfrac{Q}{A}$

Where, Q = rate of flow

A = area of cross section

Put the value into the formula

$v=\dfrac{40.0\times10^{-3}}{3.14\times(3.2\times10^{-2})^2}$

$v=12.44\ m/s$

We need to calculate the Reynolds number

Using formula of the Reynolds number

$n_{R}=\dfrac{2\rho\times v\times r}{\eta}$

Where, $\eta$ =viscosity of fluid

$\rho$ =density of fluid

Put the value into the formula

$n_{R}=\dfrac{2\times100\times12.44\times3.2\times10^{-2}}{1.002\times10^{-3}}$

$n_{R}=7.945\times10^{5}$

Hence, The Reynolds numbers for flow in the fire hose.