Try the fastest way to create flashcards
Question

# What is the pressure drop due to the Bernoulli Effect as water goes into a 3.00-cm-diameter nozzle from a 9.00-cm-diameter fire hose while carrying a flow of 40.0 L/s? (b) To what maximum height above the nozzle can this water rise? (The actual height will be significantly smaller due to air resistance.)

Solution

Verified
Step 1
1 of 3

From $\textbf{Bernoulli Equation}$ we know that :

$P_{1} + \dfrac{1}{2} \rho v_{1}^2 + \rho gh_{1}= P_{2} + \dfrac{1}{2} \rho v_{2}^2 + \rho g h_{2}$

When the two point are at the same height : it reduced to

$P_{1} + \dfrac{1}{2} \rho v_{1}^2 = P_{2} + \dfrac{1}{2} \rho v_{2}^2$

Where:

• $P_{1}$ , $P_{2}$ are the pressures at points 1, 2 .
• $\rho$ is the density of the fluid .
• $v_{1}$ ,$v_{2}$ are the velocities of the fluids at points 1,2 .

$\textbf{Givens}$ :$r_{2} = 0.015\times \mathrm{m}$ , $\rho = 1000 \mathrm{kg/m^3}$ , $r_{1} = 0.045 \mathrm{m}$ , $g= 9.8 \mathrm{m/s^2}$

$\textbf{Plugging}$ known information to get :

\begin{align*} Q&= A_{1} v_{1} \\ v_{1} &= \dfrac{Q}{A_{1}} \\ &= \dfrac{40 \times 10^{-3} }{ \pi 0.045^2} \\ &=6.29 \\ v_{2} &= \dfrac{Q}{A_{2}} \\ &= \dfrac{ 40 \times 10^{-3}}{ \pi 0.015^2} \\ &= 56.6 \end{align*}

## Recommended textbook solutions

#### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

4th EditionISBN: 9780133942651 (8 more)Randall D. Knight
3,508 solutions

#### Mathematical Methods in the Physical Sciences

3rd EditionISBN: 9780471198260 (1 more)Mary L. Boas
3,355 solutions

#### Fundamentals of Physics

10th EditionISBN: 9781118230718 (3 more)David Halliday, Jearl Walker, Robert Resnick
8,971 solutions

#### University Physics, Volume 1

1st EditionISBN: 9781938168277Jeff Sanny, Samuel J Ling, William Moebbs
1,471 solutions