A funnel of water is connected to pipes as shown in the figure. The top of the f

Question

A funnel of water is connected to pipes as shown in the figure. The top of the funnel is sufficiently large that the speed downward of the water (p = 1000 kg/m^3) at the top of the funnel is nearly zero. the water is observed to be moving at 2.0 m/s through the pipe at point b and the water is observed to exit pipe c at a speed of 2.8 m/s. Note that the pressure at point c is the atmospheric pressure.

1.) Compare the pressure at point a in the funnel with the pressure at point c in the horizontal pipe. Assume the speed at point a is 0.5 m/s.

a. Pa> Pc

b. Pa = Pc

c. Pa < Pc

2.) Calculate the difference between the pressure at point B, 2m below the surface of the water, and atmospheric pressure.

a. 1.6 * 10^4

b. 1.8 * 10^4

c. 2.0 * 10^4

d. 2.2 * 10^4

e. 2.4 * 10^4

3.) The radius of the pipe at point b is 0.15 m. what is the radius at point c?

a. 0.110 m

b. 0.127 m

c. 0.178m

Explanation / Answer

Here ,

p= 1000 Kg/m^3

vB = 2 m/s

vC = 2.8 m/s

1) as the speed of flow is higher at C than the point A

the pressure at C will be lower

hence ,a. Pa> Pc

2)

at the point B

pressure difference = p * g * h - 0.5 * p * vB^2

pressure difference = 1000 * 9.8 * 2 - 0.5 * 1000 * 2.0^2

pressure difference = 1.8 *10^4 Pa

3)

Using continuity equation ,

vC * AC = vB * AB

2 * pi * 0.15^2 = 2.8 * pi * rc^2

solving for rc

rc = 0.127 m

the radius at point C is 0.127 m

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