Question

A horizontal pipe of diameter D = 3.0 cm passes through a reservoir dam at depth d = 5.0 m. A plug secures the pipe opening. The water density is p = 1.0 x103 kg/m3. (a) Find the magnitude of the frictional force between the plug and pipe wall. (b) If the plug is removed, what water volume exits the pipe in 1.0 minute? Ignore water viscosity. (c) If the pipe is h = 10.0 m above the ground, how far will the water travel horizontally from the pipe exit when hitting the ground? Ignore air friction.

Answer 1

Given data

*The given horizontal piper of diameter is D = 3.0 cm = 0.03 m

*The given depth is d = 5.0 m

*The given water desnsity is

$p=1.0\times10^3kg/m^3$

(a)

The magnitude of the frictional force between the plug and pipe wall is given as

$\begin{gathered} F=\text{pgd}\times A \\ =\text{pgd}\times\pi r^2 \end{gathered}$

*Here r = d/2 is the radius

Substitute the values in the above expression as

$\begin{gathered} F=(1.0\times10^3)(9.8)(5.0)\times3.14\times(\frac{0.03}{2})^2 \\ =34.61\text{ N} \end{gathered}$

(b)

The volume flow rate is calculated as

$\begin{gathered} V=Av \\ =\pi r^2\sqrt[]{2gd} \\ =3.14\times(\frac{0.03}{2})^2\times\sqrt[]{2\times9.8\times5.0} \\ =6.99\times10^{-3} \end{gathered}$

The total volume is calculated as

$\begin{gathered} V_{T_{}}=V\times t \\ =6.99\times10^{-3}\times1.0\times60 \\ =0.4194m^3 \end{gathered}$