Rotameter, Variable area meter, advantages, disadvantages, applications, flow to height relation, Force balance in rotameter,diagram

A variable area meter is a meter that measures fluid flow by allowing the cross sectional area of the device to vary in response to the flow, causing some measurable effect that indicates the rate.

A rotameter is an example of a variable area meter.

Rotameter:

Some important features of Rotameters:

•  In area meters "pressure drop" is constant.
• The area through which the fluid flows varies with flow rate. The area is related through proper calibration to the flow rate.
• These rotameters can be used for liquids and gases.

Rotameter consists of a gradually tapered tube, it is arranged in vertical position. The tube contains a float, which is used to indicate the flow of the fluid. This float will be suspended in the fluid while fluid flows from bottom of the tube to top portion. The entire fluid will flow through the annular space between the tube and float. The float is the measuring element. The tube is marked with the divisions and the reading of the meter is obtained from the scale reading at the reading edge of the float. Here to convert the reading to the flow rate a calibration sheet is needed.

For higher temperatures and pressure, where glass is not going to withstand, we use metalic tapered tubes. In metalic tubes, the float is not visible so we use a rod, which is called extension, which will be used as a indicator.

floats may be constructed using different types of materials from lead to aluminium or glass or plastic. Stainless steel floats are common. According to the purpose of the meter float shape will be selected.

Advantages:

•  Pressure drop is constant
• No special fuel or external energy is required to pump
• Very easy to construct and we can use a wide variety of materials to construct.

Disadvantages:

• Due to its use of gravity, a rotameter must always be vertically oriented and right way up, with the fluid flowing upward.
•  Due to its reliance on the ability of the fluid or gas to displace the float, graduations on a given rotameter will only be accurate for a given substance at a given temperature. The main property of importance is the density of the fluid; however, viscosity may also be significant. Floats are ideally designed to be insensitive to viscosity; however, this is seldom verifiable from manufacturers' specifications. Either separate rotameters for different densities and viscosities may be used, or multiple scales on the same rotameter can be used
• Rotameters normally require the use of glass (or other transparent material), otherwise the user cannot see the float. This limits their use in many industries to benign fluids, such as water.
• Rotameters are not easily adapted for reading by machine; although magnetic floats that drive a follower outside the tube are available.

Relation between flow and meter reading: ( Force balance in rotameter)

There are three forces acting on the float.

1. Gravity force (Weight of the float)
2. Drag force ( Due to fluid flow, in the direction of flow)
3. Buoyant force ( Due to density difference beween float and water)

By balancing the above forces,

Where
F_D = Drag force
g = Acceleration due to gavity
Vf = volume of float
rho-f = Density of float
rho = Density of fluid

In the above equation the right hand side is constant, so the drag force is constant. If flow rate increases the float position must change to keep the drag force as constant.

From the definition of drag coefficient,

As the fluid is flowing through the annulus region flow is directly proportional to annular area between the float and tube.



Where D_f = Diameter of the float

                D_t = Diameter of the tube.

For linearly tapered tube with a diameter at the bottom equal to the float diameter, the area for flow is a quadratic function of the height of the float ‘h’.

By neglecting a²h² term we get a linear relationship between flow and ‘h’.

In rotameter the flow is directly proportional to the square root of the reading on the tube.