Problem 01 - Bernoulli's Energy Theorem

Problem 1
The water surface shown in Figure 4-01 is 6 m above the datum. The pipe is 150 mm in diameter and the total loss of head between point (1) in the water surface and point (5) in the jet is 3 m. Determine the velocity of flow in the pipe and the discharge Q.
 

fig_4-01_piezometer_tank.gif

 

Problem 02 - Bernoulli's Energy Theorem

Problem 2
From Figure 4-01, the following head losses are known: From (1) to (2), 0 m; from (2) to (3), 0.60 m; from (3) to (4), 2.1 m; from (4) to (5), 0.3 m. Make a table showing elevation head, velocity head, pressure head, and total head at each of the five points. How high above the center of the pipe will water stands in the piezometer tubes (3) and (4)?
 

fig_4-01_piezometer-tank_problem-2.gif

 

Problem 03 - Bernoulli's Energy Theorem

Problem 3
A 300-mm pipe is connected by a reducer to a 100-mm pipe. See Figure 4-02. Points 1 and 2 are at the same elevation, the pressure at 1 is 200 kPa. The discharge Q is 30 liters per second flowing from 1 to 2 and the energy lost from 1 to 2 is equivalent to 20 kPa.

  1. Compute the pressure at 2 if the liquid is water.
  2. Compute the pressure at 2 if the liquid is oil (sp gr = 0.80).
  3. Compute the pressure at 2 if the liquid is molasses (sp gr = 1.5).

 

fig_4-02_pipe-decreasing-pipe.gif

 

Problem 04 - Bernoulli's Energy Theorem

Problem 4
In Figure 4-02, with 15 L/s of water flowing from 1 to 2 the pressure at 1 is 100 kPa and at 2 is 70 kPa. Compute the loss of head between 1 and 2.
 

fig_4-02_pipe-decreasing-pipe_problem-4.gif

 

Problem 05 - Bernoulli's Energy Theorem

Problem 5
With 30 L/s of water flowing in Figure 4-02, what pressure must be maintained at 1 if the pressure at 2 is to be 70 kPa and the loss of head between 1 and 2 is 5 percent of the difference in pressure head at 1 and 2.
 

fig_4-02_pipe-decreasing-pipe_problem-5.gif

 

Problem 06 - Bernoulli's Energy Theorem

Problem 6
As shown in Figure 4-03, the smaller pipe is cut off a short distance past the reducer so that the jet springs free into the air. Compute the pressure at 1 if Q = 5 cfs of water. D1 = 12 inches and D2 = 4 inches. Assume that the jet has the diameter D2, that the pressure in the jet is atmospheric and that the loss of head from point 1 to point 2 is 5 ft of water.
 

fig_4-03_velocity-og-jet_solution-6.gif

 

Problem 07 - Bernoulli's Energy Theorem

Problem 7
Compute the velocity head of the jet in Figure 4-03 if D1 = 75 mm, D2 = 25 mm, the pressure head at 1 is 30 m of the liquid flowing, and the lost head between points 1 and 2 is 5 percent of the velocity head at point 2.
 

fig_4-03_velocity-of-jet.gif

 

Problem 08 - Bernoulli's Energy Theorem

Problem 8
In Figure 4-04, with 35 L/s of sea water (sp gr 1.03) flowing from 1 to 2, the pressure at 1 is 100 kPa and at 2 is -15 kPa. Point 2 is 6 m higher than point 1. Compute the lost energy in kPa between 1 and 2.
 

fig_4-04_decreasing-diameter-pipe.gif

 

Problem 09 - Bernoulli's Energy Theorem

Problem 9
The diameter of a pipe carrying water changes gradually from 150 mm at A to 450 mm at B. A is 4.5 m lower than B. What will be the difference in pressure, in kPa, between A and B, when 0.176 m3/s is flowing, loss of energy is being neglected.
 

fig_problem-09_inclined-tapering-pipe.gif

 

Problem 10 - Bernoulli's Energy Theorem

Problem 10
The diameter of a pipe carrying water changes gradually from 150 mm at A to 450 mm at B. A is 4.5 m lower than B. If the pressure at A is 70 kPa and that B is 50 kPa, when 140 L/s is flowing.
(a) Determine the direction of flow.
(b) Find the frictional loss between the two points.
 

fig_problem-10_tapering-pipe.gif

 

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