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

  • Thread starter Thread starter Coushander
  • Start date Start date
  • Tags Tags
    Paint
AI Thread Summary
The diameter of the constriction in a paint sprayer significantly impacts its operation by affecting air pressure and flow dynamics. In this scenario, the air speed in the 2.50-cm diameter pipe is 5.00 m/s, leading to a pressure drop that allows paint to rise through the feed tube. Using the principle of incompressible fluid flow, the calculations show that the maximum diameter of the constriction should be approximately 8.07 mm for optimal performance. This ensures that the pressure remains balanced between the top and bottom of the tube, allowing efficient paint delivery. Proper understanding of these dynamics is crucial for effective paint sprayer design and operation.
Coushander
Messages
27
Reaction score
0

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
 
Physics news on Phys.org
Double r obviously. I had that thought while I was eating a sandwich.

d = 8.08mm (correct within rounding)
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'Calculation of Tensile Forces in Piston-Type Water-Lifting Devices at Elevated Locations'

Thread 'Calculation of Tensile Forces in Piston-Type Water-Lifting Devices at Elevated Locations'

Figure 1 Overall Structure Diagram Figure 2: Top view of the piston when it is cylindrical A circular opening is created at a height of 5 meters above the water surface. Inside this opening is a sleeve-type piston with a cross-sectional area of 1 square meter. The piston is pulled to the right at a constant speed. The pulling force is（Figure 2）： F = ρshg = 1000 × 1 × 5 × 10 = 50,000 N. Figure 3: Modifying the structure to incorporate a fixed internal piston When I modify the piston...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

Continuity Equation Homework: Diameter of Constriction
Replies
11
Views
5K
How Do Fluid Dynamics Affect Medical and Environmental Applications?
Replies
1
Views
5K
How Does Constriction in the Bronchus Affect Air Pressure?
Replies
2
Views
10K
How Much Power Does a 30m Diameter Windmill Generate?
Replies
1
Views
11K
Manometer Oil Problem: How to Calculate Water Level Difference | Expert Help
Replies
14
Views
7K
Archived How Does Air Flow Affect Pressure and Velocity in a Venturi Tube?
Replies
1
Views
9K
How Does Blood Pressure Change with Velocity in Fluid Mechanics?
Replies
2
Views
2K
How Does Pipe Configuration Affect Pressure in a Fluid System?
Replies
3
Views
2K
How does Boyles law apply to air in motion in a uniform tube?
Replies
2
Views
2K
How Does Changing Gas Quantity and Temperature Affect Pressure?
Replies
10
Views
10K

Hot Threads

Recent Insights

Back
Top