#### Question

Oil with a density of $850 kg/m^3$ and kinematic viscosity of $0.00062 m^2/s$ is being discharged by a 8-mm-diameter, 40-m-long horizontal pipe from a storage tank open to the atmosphere. The height of the liquid level above the center of the pipe is 4 m. Disregarding the minor losses, determine the flow rate of oil through the pipe.

#### Solution

Verified#### Step 1

1 of 4$\textbf{Given:}$

$\rho = 850 \dfrac{kg}{m^3}$

$\nu = 62 \times 10^{-5} \dfrac{m^2}{s}$

$D = 0.008$ $m$

$L = 40$ $m$

$h = 4$ $m$

$\textbf{Approach:}$

We have steady and incompressible flow. The entrance effects are negligible, so the flow is fully developed. The entrance and exit loses are alos negligible.

First step is to calculate pressure at the bottom of the tank:

$\begin{align*} P_{1,gage} &= \rho g h = 850 \cdot 9.81 \cdot 4\\ &= 33.354 kPa \end{align*}$

Disregarding inlet and outlet losses, the pressure drop across the pipe is:

$\begin{align*} \Delta P &= P_1 - P_2 = P_1 - P_{atm} = P_{1,gage}\\ &=\boxed{33.354 Pa}\\ \end{align*}$