Pressure with fluid problem

In summary, the first conversation is about calculating the excess pressure required along a hypodermic needle to achieve a flow rate of 1 g/s for water. The answer should be in units of Pa. The second conversation is about determining the pressure drop in a constriction in the bronchus, assuming incompressible flow, where the average flow speed of air doubles. The answer should also be in units of Pa. The third conversation involves finding the radius of a pipe carrying water from a 25.0 m tall tank to a remote town, given a distance of 3.15 x 10^2 km and a desired volume flow rate of at least 0.0500 m^3/s. The answer should be
  • #1
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1.) A hypodermic needle is 3.2 cm in length and 0.32 mm in diameter. What excess pressure is required along the needle so that the flow rate of water through it will be 1 g/s?

answer should be in units Pa

2.) When a person inhales, air moves down the bronchus (windpipe) at 14 cm/s. The average flow speed of the air doubles through a constriction in the bronchus. Assuming incompressible flow, determine the pressure drop in the constriction.

answer should be in units Pa

3.) A pipe carrying water from a tank 25.0 m tall must cross 3.15 102 km of wilderness to reach a remote town. Find the radius of the pipe so that the volume flow rate is at least 0.0500 m3/s. (Use the viscosity of water at 20°C.)

answer should be in units of Meters
 
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  • #2
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  • #3


1.) To calculate the excess pressure required for a flow rate of 1 g/s through a hypodermic needle, we can use the Hagen-Poiseuille equation:

Q = (πΔPr^4)/(8ηL)

Where Q is the flow rate, ΔP is the pressure difference, r is the radius of the needle, η is the viscosity of water, and L is the length of the needle.

Rearranging the equation, we get:

ΔP = (8ηQL)/(πr^4)

Substituting the given values, we get:

ΔP = (8 * 0.001 * 0.032)/(π * 0.00016^4) = 318,309.89 Pa

Therefore, an excess pressure of approximately 318,309.89 Pa is required along the needle for a flow rate of 1 g/s.

2.) According to the Bernoulli's equation, the pressure drop in a constriction can be calculated as:

ΔP = (ρV^2)/2

Where ρ is the density of air and V is the velocity of air.

Since the average flow speed of air doubles through the constriction, we can write:

V = 2 * 14 cm/s = 28 cm/s = 0.28 m/s

Substituting the values, we get:

ΔP = (1.225 kg/m^3 * 0.28^2)/2 = 0.048 Pa

Therefore, the pressure drop in the constriction is approximately 0.048 Pa.

3.) The volume flow rate through a pipe can be calculated as:

Q = (πr^4ΔP)/(8ηL)

Where Q is the volume flow rate, r is the radius of the pipe, ΔP is the pressure difference, η is the viscosity of water, and L is the length of the pipe.

Rearranging the equation, we get:

r = ∛((8ηLQ)/(πΔP))

Substituting the given values, we get:

r = ∛((8 * 0.00089 * 0.050)/(π * 3.15 * 10^5 * 25)) = 0.00113 m

Therefore, the radius of the pipe should be approximately 0.00113 m to achieve a volume
 

What is pressure with fluid problem?

Pressure with fluid problem refers to a type of problem in physics that involves analyzing the pressure exerted by a fluid on a surface or within a container. This type of problem is commonly encountered in fields such as fluid mechanics, hydraulics, and aerodynamics.

What is the equation for calculating pressure with fluid problem?

The equation for calculating pressure with fluid problem is P = F/A, where P is the pressure, F is the force applied by the fluid, and A is the area over which the force is applied. This equation is known as Pascal's Law and is used to determine the pressure at a specific point in a fluid.

What factors affect pressure in a fluid?

The pressure in a fluid is affected by several factors, including the density of the fluid, the depth or height of the fluid, and the acceleration due to gravity. Other factors such as temperature, viscosity, and the shape of the container can also impact the pressure in a fluid.

How is pressure different from force?

While pressure and force are related, they are not the same thing. Pressure is the amount of force per unit area, while force is a measure of the strength or intensity of a push or pull. In other words, pressure is the distribution of force over an area, whereas force is the total amount of energy exerted on an object.

What are some real-world applications of pressure with fluid problem?

Pressure with fluid problem has many real-world applications, such as hydraulic systems used in heavy machinery and vehicles, aerodynamics of airplanes and cars, and the functioning of pumps and turbines. Understanding pressure with fluid problem is also crucial in fields like meteorology, oceanography, and geology.

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