LIQUIDS IN MOTION
In the operation of fluid power systems, theremust be a flow of fluid. The amount of flow will vary from system to system. To understand fluid power systems in action, it is necessary to understand some of the characteristics of liquids in motion.
Liquids in motion have characteristics differentfrom liquids at rest. Frictional resistances within a fluid (viscosity) and inertia contribute to these differences. (Viscosity is discussed in chapter 3.) Inertia, which means the resistance a mass offers to being set in motion, will be discussed later in this section. There are other relationships of liquids in motion with which you must become familiar. Among these are volume and velocity of flow, flow rate and speed, laminar and turbulent flow, and more importantly, the force and energy changes which occur in flow.
VOLUME AND VELOCITY OF FLOW
The volume of a liquid passing a point in agiven time is known as its volume of flow or flow rate. The volume of flow is usually expressed in gallons per minute (gpm) and is associated with relative pressures of the liquid, such as 5 gpm at 40 psi.
The velocity of flow or velocity of the fluidis defined as the average speed at which the fluid moves past a given point. It is usually expressed in feet per second (fps) or feet per minute (fpm). Velocity of flow is an important consideration in sizing the hydraulic lines. (Hydraulic lines are discussed in chapter 5.)
Volume and velocity of flow are oftenconsidered together. With other conditions unaltered—that is, with volume of input unchanged—the velocity of flow increases as the cross section or size of the pipe decreases, and the velocity of flow decreases as the cross section increases. For example, the velocity of flow is slow at wide parts of a stream and rapid at narrow parts, yet the volume of water passing each part of the stream is the same.
In figure 2-13, if the cross-sectional area ofthe pipe is 16 square inches at point A and 4 square inches at point B, we can calculate the relative velocity of flow using the flow equation
Q =vA Equation 2-7.
where Q is the volume of flow, v is the velocityof flow and A is the cross-sectional area of the liquid. Since the volume of flow at point A, Q1, is equal to the volume of flow at point B, Q2, we can use equation 2-7 to determine the ratio of the
Figure 2-13.—Volume and velocity of flow.
velocity of flow at point A, v1, to the velocity of flow at point B, v2. Since Q1 = Q2, A1v 1 = A2v 2 From figure 2-13; A1 = 16sq. in., A2 = 4sq. in. Substituting: 16v1 = 4V 2 or v2 = 4vI Therefore, the velocity of flow at point B is four times the velocity of flow at point A.
VOLUME OF FLOW AND SPEED
If you consider the cylinder volume you must fill and the distance the piston must travel, you can relate the volume of flow to the speed of the piston. The volume of the cylinder is found by multiplying the piston area by the length the piston must travel (stroke).
Suppose you have determined that two cylinders have the same volume and that one cylinder is twice as long as the other. In this case, the cross-sectional area of the longer tube will be half of the cross-sectional area of the other tube. If fluid is pumped into each cylinder at the same rate, both pistons will reach their full travel at the same time. However, the piston in the smaller cylinder must travel twice as fast because it has twice as far to go.
There are two ways of controlling the speed of the piston, (1) by varying the size of the cylinder and (2) by varying the volume of flow (gpm) to the cylinders. (Hydraulic cylinders are discussed in detail in chapter 10. )
STREAMLINE AND TURBULENT FLOW
At low velocities or in tubes of small diameter, flow is streamlined. This means that a given particle of fluid moves straight forward without bumping into other particles and without crossing their paths. Streamline flow is often referred to as laminar flow, which is defined as a flow situation in which fluid moves in parallel lamina or layers. As an example of streamline flow, consider figure 2-14, which illustrates an open stream flowing at a slow, uniform rate with logs floating on its surface. The logs represent particles of fluid. As long as the stream flows at a slow, uniform rate, each log floats downstream in its own path, without crossing or bumping into the other.
Figure 2-14.—Streamline flow.
If the stream narrows, however, and the volume of flow remains the same, the velocity of flow increases. If the velocity increases sufficiently, the water becomes turbulent. (See fig. 2-15.) Swirls, eddies, and cross-motions are set up in the water. As this happens, the logs are thrown against each other and against the banks of the stream, and the paths followed by different logs will cross and recross.
Particles of fluid flowing in pipes act in the same manner. The flow is streamlined if the fluid flows slowly enough, and remains streamlined at greater velocities if the diameter of the pipe is small. If the velocity of flow or size of pipe is increased sufficiently, the flow becomes turbulent. While a high velocity of flow will produce turbulence in any pipe, other factors contribute to turbulence. Among these are the roughness of the inside of the pipe, obstructions, the degree of curvature of bends, and the number of bends in the pipe. In setting up or maintaining fluid power systems, care should be taken to eliminate or minimize as many causes of turbulence as possible, since the energy consumed by turbulence is wasted. Limitations related to the degree and number of bends of pipe are discussed in chapter 5.
Figure 2-15.—Turbulent flow.
While designers of fluid power equipment do what they can to minimize turbulence, it cannot be avoided. For example, in a 4-inch pipe at 68°F, flow becomes turbulent at velocities over approximately 6 inches per second or about 3 inches per second in a 6-inch pipe. These velocities are far below those commonly encountered in fluid power systems, where velocities of 5 feet per second and above are common. In streamlined flow, losses due to friction increase directly with velocity. With turbulent flow these losses increase much more rapidly.