Question

Assume that water flowing through a pipe with a circular cross section flows most rapidly at...

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.

Homework Answers

Answer #1

So the ?vdA = Q where Q is the volumetric flow rate.

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

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Water flows through a circular pipe with a radius of 10 cm at 12 m/s. (a)...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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?