Question

Assume that water flowing through a pipe with a circular cross section flows most rapidly at the center of the pipe and least rapidly near the pipe walls (this might be reasonable because of friction between the water and the pipe walls). Assume that the water speed at the walls is half as great as the speed at the center, and assume that the decrease is linear (i.e. the graph of water speed versus radius is a straight line). If the radius of the pipe is 18.0 cm and if the volume flux of water is 8.00 liters per second, find the speed of the water at the center of the pipe. (One liter is 1000 cubic centimeters or 0.001 cubic meters). Hint: Draw the graph of speed versus radius, and then do the integral for the volume flux of water through the tube symbolically. Finally, use the given values to solve for the unknown water speed at the pipe center.

Answer #1

The relationship between r and v is the slope 1-r/2*(R) where R is
0.18 m.

So you'll get something like:

?[0,2*pi],[0,.18] of v(1-r/.2)rdrd(theta) = .008

v is technically a constant that you would multiply to get your
velocity and is therefore the thing you want to solve for since v
will be it's greatest in the center anyway. Oh and theta has no
angular dependence so we can take that out.

2*pi*v* ?[0,.18] of r-r^2/.20 dr = .008

solve for the rest and your answer is:

v= 3.654 e-1 m/s

Water flows through a circular pipe with a radius of 10 cm at 12
m/s. (a) If the radius of the pipe increases to 20 cm, what is the
new speed of the water in the pipe? (b) Does the volume flow rate
or the mass flow rate change in the pipe? (c) Calculate both the
volume flow rate and mass flow rate in the pipe?

Water flowing out of a horizontal pipe emerges through a nozzle.
The radius of the pipe is 2.3 cm, and the radius of the nozzle is
0.41 cm. The speed of the water in the pipe is 0.74 m/s. Treat the
water as an ideal fluid, and determine the absolute pressure of the
water in the pipe.

Water flowing out of a horizontal pipe emerges through a nozzle.
The radius of the pipe is 1.8 cm, and the radius of the nozzle is
0.51 cm. The speed of the water in the pipe is 0.70 m/s. Treat the
water as an ideal fluid, and determine the absolute pressure of the
water in the pipe.

The pressure of water flowing through a 6.3×10?2 ?m
-radius pipe at a speed of 1.1 m/s is 2.2 ×105 N/m2.
(a) What is the flow rate of water?
(b) What is the pressure in the water after it goes up a 4.6 ?m
-high hill and flows in a 5.0×10?2 ?m-radius pipe?

The water flowing through a 1.7 cm (inside diameter) pipe flows
out through three 1.3 cm pipes. (a) If the flow rates in the three
smaller pipes are 26, 19, and 12 L/min, what is the flow rate in
the 1.7 cm pipe? (b) What is the ratio of the speed of water in the
1.7 cm pipe to that in the pipe carrying 26 L/min?

The water flowing through a 2.0 cm (inside diameter) pipe flows out
through three 1.4 cm pipes. (a) If the flow rates
in the three smaller pipes are 24, 15, and 11 L/min, what is the
flow rate in the 2.0 cm pipe? (b) What is the
ratio of the speed of water in the 2.0 cm pipe to that in the pipe
carrying 24 L/min?

The pressure of water flowing through a 5.9×10^-2 m-radius pipe
at a speed of 1.2 m/s is 2.2×10^5 N/m^2.
a) What is the flow rate of the water?
b) What is the pressure in the water after it goes up a 5.8
m-high hill and flows in a 4.2×10^-2 m-radius pipe?

Water flowing through a 1.3 cm -diameter pipe can fill a 300 L
bathtub in 5.6 min . Part A What is the speed of the water in the
pipe? show work please.
The gauge pressure at the bottom of a cylinder of liquid is 0.30
atm . The liquid is poured into another cylinder with twice the
radius of the first cylinder.
What is the gauge pressure at the bottom of the second cylinder?
answer with 2 sig figs.

Q9:
The pressure of water flowing through a 6.2×10−2-m-radius pipe
at a speed of 1.5 m/s is 2.2×105N/m2.
Part A:
What is the flow rate of the water?
Express your answer with the appropriate units.
Part B:
What is the pressure in the water after it goes up a 6.0-m-high
hill and flows in a 4.6×10−2-m-radius pipe?
Express your answer with the appropriate units.

water flows steadily from the left pipe section (radius
r1 = 2.00R), through the middle
section (radius R = 0.0106 m), and into the right section
(radius r3 = 3.00R). The speed of the
water in the middle section is 0.402 m/s. What is the net work done
on 0.310 m3 of the water as it moves from the left to
the right section?

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