How Does the Diameter of Constriction Affect a Paint Sprayer's Operation?

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In summary, a paint sprayer uses a constricted area in a 2.50-cm diameter pipe to pump air and cause a drop in pressure, allowing paint to rise up the feed tube and enter the air stream. The maximum diameter of the constriction that will allow the sprayer to operate is 8.07mm. This can be determined using equations for incompressible ideal fluids and taking into account the density and speed of the air and paint.
  • #1
Coushander
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Homework Statement



A paint sprayer pumps air through a constriction in a 2.50-cm diameter pipe, as shown in the figure. The flow causes the pressure in the constricted area to drop and paint rises up the feed tube and enters the air stream. The speed of the air stream in the 2.50-cm diameter sections is 5.00 m/s. The density of the air is 1.29 kg/m3, and the density of the paint is 1200 kg/m3. We can treat the air and paint as incompressible ideal fluids. What is the maximum diameter of the constriction that will allow the sprayer to operate?

p12.38.jpg


Correct Answer = 8.07mm

Homework Equations



ρvA = constant (any fluid)

vA = constant (incompressible fluid)

p + (1/2)ρv2 + ρgy = constant

The Attempt at a Solution



Area at 2.5cm section = (pi)(r)2 = (pi)(0.0125m)2 = 4.91 x 10-4m2

Pressure at bottom of 12.5cm tube = (1200 kg/m3)(9.81m/s2)(0.125m) = 1471.5 N/m2 (Pa)

Pressure at bottom of tube = pressure at top of tube

1471.5 Pa = (1/2)(ρ)(v2)

v = 47.76 m/s

(constant at wide portion) vA = vA (constant at constricton)

A = A (v/v) = 5.14 x 10-5 m2

r = 4.04 x 10-3 m = 4.04mm
 
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  • #2
Double r obviously. I had that thought while I was eating a sandwich.

d = 8.08mm (correct within rounding)
 

FAQ: How Does the Diameter of Constriction Affect a Paint Sprayer's Operation?

What is a paint sprayer constriction?

A paint sprayer constriction refers to the size of the opening or nozzle on a paint sprayer that controls the flow of paint. A smaller constriction results in a finer spray, while a larger constriction produces a thicker spray.

Why is the paint sprayer constriction important?

The paint sprayer constriction is important because it determines the type of finish and coverage you will achieve when using the sprayer. It also affects the amount of overspray and the speed at which you can complete a project.

How do I choose the right paint sprayer constriction?

The right paint sprayer constriction depends on the type of paint you are using and the surface you are painting. For thinner paints and smaller surfaces, a smaller constriction is recommended, while thicker paints and larger surfaces may require a larger constriction.

Can I change the paint sprayer constriction?

Yes, most paint sprayers allow you to change the constriction by switching out the nozzle or adjusting the settings on the sprayer. However, it is important to follow the manufacturer's instructions and guidelines for proper use and maintenance.

How do I clean a paint sprayer constriction?

To clean a paint sprayer constriction, you should follow the manufacturer's instructions and use the recommended cleaning solution. Typically, you will need to disassemble the sprayer and soak the parts in the solution before rinsing and reassembling. Regular cleaning of the constriction can help maintain the sprayer's performance and prolong its lifespan.

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