Calculate the smaller section's pressure

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In summary, we have a liquid flowing through two horizontal sections of tubing with different cross-sectional areas and flow speeds. Using the given information, we can calculate the smaller section's flow speed to be 7.67m/s and its pressure to be 1.2184x10^5 Pa.
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Sunsing
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Homework Statement



A liquid (p = 1.65 g/cm3) flows through two horizontal sections of tubing joined end to end. In the first section the cross-sectional area is 10.0 cm2, the flow speed is 265 cm/s, and the pressure is 1.20 x10^5 Pa. In the second section the cross-sectional area is 3.50 cm2.

a) Calculate the smaller section's flow speed. 7.67m/s

(b) Calculate the smaller section's pressure. ?

Homework Equations



p=1.65g/cm^3 =.00165kg/cm^3
A1=10cm^2
v1=265cm/s
P1=1.2x10^5pa
A2=3.5cm^2
V2=7.67m/s = 767cm/s
P2=?

P1+1/2pv1^2=P2+1/2pv2^2

The Attempt at a Solution



I'm getting an incorrect answer for P2 in question b, but I'm not sure what I'm doing wrong.

I got 1.19**10^5, but that is incorrect. Any ideas?

Thank you
 
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  • #2
!P2=P1+1/2p(v1^2-v2^2)P2=1.2x10^5+1/2(.00165)(265^2-767^2)P2=1.2x10^5+1/2(.00165)(709025-589693)P2=1.2x10^5+1/2(.00165)(111332)P2=1.2x10^5+1858.2P2=1.2184x10^5 Pa
 
  • #3
for your question. To calculate the smaller section's pressure, we can use the Bernoulli's equation, which states that the total pressure at any point in a fluid is equal to the sum of the static pressure and the dynamic pressure. Static pressure is the pressure exerted by the fluid at rest, while dynamic pressure is the pressure exerted by the fluid in motion.

Using this equation, we can rewrite it as:

P1 + 1/2ρv1^2 = P2 + 1/2ρv2^2

Where P1 and v1 are the pressure and velocity in the first section, and P2 and v2 are the pressure and velocity in the second section.

Substituting the given values, we get:

1.20 x 10^5 Pa + 1/2(1.65 x .00165)(265 cm/s)^2 = P2 + 1/2(1.65 x .00165)(767 cm/s)^2

Solving for P2, we get:

P2 = 1.19 x 10^5 Pa

Therefore, the smaller section's pressure is 1.19 x 10^5 Pa.

I hope this helps clarify the solution. If you continue to have trouble, please let me know and I can walk you through the steps in more detail.
 

1. What is the formula for calculating pressure?

The formula for calculating pressure is pressure = force/area, where force is measured in newtons and area is measured in square meters.

2. How do you calculate the smaller section's pressure?

To calculate the smaller section's pressure, you will need to know the force acting on the smaller section and its corresponding surface area. Once you have these values, you can use the formula pressure = force/area to calculate the smaller section's pressure.

3. Can you give an example of calculating the smaller section's pressure?

Sure, let's say there is a force of 50 newtons acting on a smaller section with a surface area of 2 square meters. Using the formula pressure = force/area, we can calculate the smaller section's pressure to be 25 newtons per square meter.

4. What units are used to measure pressure?

Pressure can be measured in various units, including pascals (Pa), newtons per square meter (N/m²), and pounds per square inch (psi). It is important to make sure all values used in the calculation are in the same unit of measurement.

5. How is pressure related to force and area?

Pressure is directly proportional to force and inversely proportional to area. This means that as the force acting on a surface increases, the pressure also increases. Conversely, as the surface area increases, the pressure decreases.

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