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.
 

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.
 

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).

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)?
 

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.
 

Energy is defined as ability to do work. Both energy and work are measured in Newton-meter (or pounds-foot in English). Kinetic energy and potential energy are the two commonly recognized forms of energy. In a flowing fluid, potential energy may in turn be subdivided into energy due to position or elevation above a given datum, and energy due to pressure in the fluid. Head is the amount of energy per Newton (or per pound) of fluid.
 

Kinetic Energy and Velocity Head
Kinetic energy is the ability of a mass to do work by virtue of its velocity. The kinetic energy of a mass M having a velocity v is ½Mv². Since M = W/g,

Elevation Energy and Elevation Head
In connection to the action of gravity, elevation energy is manifested in a fluid by virtue of its position or elevation with respect to a horizontal datum plane.

Pressure Energy and Pressure Head
A mass of fluid acquires pressure energy when it is in contact with other masses having some form of energy. Pressure energy therefore is an energy transmitted to the fluid by another mass that possesses some energy.

Problem
The diameter of a 6-m length pipe decreases uniformly from 450 mm to 150 mm. With a flow of 0.15 m³/sec of oil, compute the mean velocity at cross section 1 m apart. Plot the velocity as ordinate against length as abscissa.
 

Graph of velocity of flow versus length of pipe (plotted in MS Excel)

Problem 1
Compute the discharge of water through 75 mm pipe if the mean velocity is 2.5 m/sec.
 

Problem 2
The discharge of air through a 600-mm pipe is 4 m³/sec. Compute the mean velocity in m/sec.
 

Problem 3
A pipe line consists of successive lengths of 380-mm, 300-mm, and 250-mm pipe. With a continuous flow through the line of 250 Lit/sec of water, compute the mean velocity in each size of pipe.
 

Discharge (also called flow rate)
The amount of fluid passing a section of a stream in unit time is called the discharge. If v is the mean velocity and A is the cross sectional area, the discharge Q is defined by Q = Av which is known as volume flow rate. Discharge is also expressed as mass flow rate and weight flow rate.

Problem
A closed cylindrical vessel 3 m. in diameter and 6 m high is filled with water to a height of 4.5 m. The rest is filled with air, the pressure of which is 105 kPa. If the vessel is rotated at 191 rpm about its axis, determine the maximum and minimum inside pressure at the base.