Calculate Volume Flow Rate: Hose Diam & Cliff Height

In summary, the local fire brigade has requested the setup of a pump system to draw seawater from the ocean to the top of a 12.0 m high cliff. The available pump can produce a gauge pressure of 150 kPa and a hose with a radius of 4.00 cm can pump water at a rate of 40.4 L/s. Doubling the diameter of the hose would result in a volume flow rate of 2 times the original rate. The relevant equations for this problem include Iv = pi r^2 for volume flow rate, and Bernoulli's equation simplified as v = square root of: (gauge pressure - density of water*g*height)/(1/2 density).
  • #1
sonutulsiani
138
0

Homework Statement




To better fight fires in your seaside community, the local fire brigade has asked you to set up a pump system to draw seawater from the ocean to the top of a steep cliff adjacent to the water where most of the homes are.

1. If the cliff is 12.0 m high, and the pump is capable of producing a gauge pressure of 150 kPa, how much water (in L/s) can be pumped using a hose with a radius of 4.00 cm?

A. Iv = 40.4 L/s
B. Iv = 45.0 L/s
C. Iv = 32.8 L/s
D. Iv = 13.6 L/s

2. How would the volume flow rate change if the diameter of the hose were doubled?

A. Iv, new = ½ Iv, old
B. Iv, new = Iv, old
C. Iv, new = 2 Iv, old
D. Iv, new = 4 Iv, old

(Iv is volume flow rate)


Homework Equations





The Attempt at a Solution



I know Iv=pi r^2, what else?
I also know 2nd question will be equal but just want to make sure.
 
Physics news on Phys.org
  • #2
Volume Flow Rate: Iv=Av
Bernoulli equation simplified: v = square root of: (Gauge Pressure - density of water*g*height)/(1/2 density)
 
  • #3


Based on the given information, we can calculate the volume flow rate using the formula Iv = A*V, where A is the cross-sectional area of the hose and V is the velocity of the water.

1. To calculate the cross-sectional area, we need to convert the radius of the hose from centimeters to meters. Therefore, A = pi*(0.04m)^2 = 0.005 m^2.

Next, we can use Bernoulli's equation to find the velocity of the water at the top of the cliff, given the gauge pressure of 150 kPa and the height of 12.0 m. Using the equation P1 + 1/2*p*v1^2 + p*g*h1 = P2 + 1/2*p*v2^2 + p*g*h2, where P is pressure, p is density, v is velocity, and h is height, we can rearrange the equation to solve for v2, the velocity at the top of the cliff.

P1 = atmospheric pressure (101.325 kPa)
P2 = gauge pressure (150 kPa)
p = density of water (1000 kg/m^3)
h1 = height at sea level (0 m)
h2 = height at top of cliff (12.0 m)

Substituting the values into the equation, we get:

101.325 kPa + 0 + (1000 kg/m^3)(9.8 m/s^2)(0 m) = 150 kPa + 0 + (1000 kg/m^3)(9.8 m/s^2)(12.0 m) + (1000 kg/m^3)(v2)^2

Rearranging and solving for v2, we get:

v2 = 14.7 m/s

Now, we can plug in the values for A and v into the formula for volume flow rate to get:

Iv = (0.005 m^2)(14.7 m/s) = 0.0735 m^3/s

To convert to liters per second, we can multiply by 1000 (1 m^3 = 1000 L):

Iv = 73.5 L/s

Therefore, the correct answer is option B, 73.5 L/s.

2. If the diameter of the hose is doubled, the new radius will be 2 times the original radius
 

1. What is volume flow rate?

Volume flow rate is the amount of fluid that passes through a given point in a certain amount of time. It is typically measured in liters per second (L/s), cubic meters per second (m3/s), or gallons per minute (gpm).

2. How do you calculate volume flow rate?

To calculate volume flow rate, you need to know the cross-sectional area of the hose and the velocity of the fluid. Multiply the area by the velocity to get the volume flow rate. The formula is Q = A x V, where Q is the volume flow rate, A is the cross-sectional area, and V is the velocity.

3. What is the relationship between hose diameter and volume flow rate?

The volume flow rate is directly proportional to the hose diameter. This means that as the diameter of the hose increases, the volume flow rate also increases. This is because a larger diameter allows for more fluid to flow through at a given velocity.

4. How does the height of the cliff affect the volume flow rate?

The height of the cliff does not directly affect the volume flow rate. However, the height may affect the velocity of the fluid as it falls from the cliff. The greater the height, the greater the velocity will be, which will increase the volume flow rate.

5. What are some real-world applications of calculating volume flow rate?

Calculating volume flow rate is useful in many industries, including plumbing, irrigation, and HVAC. It is also important in environmental engineering for measuring water flow in rivers and streams. Additionally, volume flow rate is used in chemical and industrial processes to ensure proper flow and distribution of fluids.

Similar threads

  • Introductory Physics Homework Help
Replies
4
Views
3K
  • Introductory Physics Homework Help
Replies
1
Views
1K
Replies
5
Views
3K
Replies
3
Views
6K
  • Mechanical Engineering
Replies
8
Views
731
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
7K
  • Introductory Physics Homework Help
Replies
4
Views
3K
Replies
2
Views
3K
  • Mechanical Engineering
Replies
3
Views
5K
Back
Top