Question

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?

Answer #1

Density of water = = 1000
kg/m^{3}

Gravitational acceleration = g = 9.81 m/s^{2}

Pressure at point 1 = P_{1} = 2.2 x 10^{5}
N/m^{2} = 220000 N/m^{2}

Radius of the pipe at point 1 = R_{1} = 5.9 x
10^{-2} m

Speed of flow at point 1 = V_{1} = 1.2 m/s

Area of the pipe at point 1 = A_{1} = R_{1}^{2}

Pressure at point 2 = P_{2}

Radius of the pipe at point 2 = R_{2} = 4.2 x
10^{-2} m^{2}

Speed of flow at point 2 = V_{2}

Height of point 2 compared to point 1 = h = 5.8 m

Area of the pipe at point 2 = A_{2} = R_{2}^{2}

Flow rate of water = Q

Q = A_{1}V_{1}

Q = R_{1}^{2}V_{1}

Q = (5.9x10^{-2})^{2}(1.2)

Q = 1.312 x 10^{-2} m^{3}/s

By continuity equation,

A_{1}V_{1} = A_{2}V_{2}

R_{1}^{2}V_{1}
= R_{2}^{2}V_{2}

R_{1}^{2}V_{1} =
R_{2}^{2}V_{2}

(5.9x10^{-2})^{2}(1.2) =
(4.2x10^{-2})V_{2}

V_{2} = 2.368 m/s

By bernoulli's equation,

P_{2} = 161018.29 N/m^{2}

a) Flow rate of water = 1.312 x 10^{-2}
m^{3}/s

b) Pressure in the water after it goes up a 5.8 m high hill and
flows in a 4.2x10^{-2}m radius pipe = 161018.29
N/m^{2}

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?

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.

A pipe of radius 10 cm has a pressure of 1.2 x 105 N/m2 as it
goes up to a second floor 3.1 m up, it decreases in size to a
radius of 5 cm and a water speed of 8.0 m/s
Find the water speed in the first part of the pipe.
Find the pressure in the second part 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 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.

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?

Given: The viscosity is negligible. Atmospheric pressure is
101300 Pa. Water flows at speed of 5.9 m/s through a horizontal
pipe of diameter 3.3 cm. The gauge pressure P1 of the water in the
pipe is 1.6 atm. A short segment of the pipe is constricted to a
smaller diameter of 2.4 cm.
What is the gauge pressure of the water flowing through the
constricted segment? Answer in units of atm.

A horizontal pipe contains water at a pressure of 100 kPa
flowing with a speed of 2.0 m/s . The pipe narrows to one-half its
original diameter.
The speed of the water is 8 m/s
what is the pressure of the water?

There is a pipe with a radius of 47 cm. Water is flowing thorugh
this pipe and ends up 4.7 m below the starting point with a radius
of 83 cm. The water enters at the starting point with a velcity of
4.9 m/s. What is the pressure difference between the starting point
and endpoint of the pipe assuming that the density of water is 1000
kg/m^3.

A 4.70 cm radius pipe has ethanol flowing through it at 6.00
m/s. The pipe then rises by 7.00 m and increases in radius to 11.3
cm. The pipe then empties into the air.
(a) What is the pressure within the ethanol in the first 4.70 cm
radius segment?
____ Pa
(b) How fast is the ethanol in the second 11.3 cm radius
segment?
___ m/s

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