## Micromanometer

**Micromanometer** Assignment Help | **Micromanometer** Homework Help

# Micromanometer

(1) Single Column Manometer:

• Single column manometer is a modified form of a U-tube manometer

• Due to large cross-sectional area of the reservoir, for any change in pressure, the change in the liquid level in the reservoir will be very small which may be neglected and hence the pressure is given by the height of liquid in the other limb.

• The other limb may be vertical or inclined. Thus there are two type soft single column manometer as:

(a) Vertical Single Column Manometer (b) Inclined Single Column Manometer

• Single column manometer is a modified form of a U-tube manometer

• Due to large cross-sectional area of the reservoir, for any change in pressure, the change in the liquid level in the reservoir will be very small which may be neglected and hence the pressure is given by the height of liquid in the other limb.

• The other limb may be vertical or inclined. Thus there are two type soft single column manometer as:

(a) Vertical Single Column Manometer (b) Inclined Single Column Manometer

## (a) Vertical Single Column Manometer:

Let dh = Fall of heavy liquid in reservoir

h

_{1}= Height of light center pipe above X-X

h

_{2}= Rise of heavy liquid in right limb

P

_{A}= Pressure at A, which is to be measured

A = Cross-sectional area of the reservoir

a = Cross-sectional area of the reservoir

S

_{1}= Specific gravity of liquid in pipe

S

_{2}= Specific gravity of heavy liquid in reservoir and right limb

ρ

_{1}= Density of liquid in pipe

ρ

_{2}= Density of liquid in reservoir

Fall of heavy liquid in reservoir will cause a rise of heavy liquid level in the right limb

A x dh = a x h

_{2}

dh = a x h

_{2}/ A

Now consider the datum line Y-Y as shown in. Then by static equilibrium Pressure in the left limb above Y-Y = Pressure in the right limb above Y-Y

ρ

_{1}x g x (dh + h

_{1}) + P

_{A}= ρ

_{2 }x g x (dh + h

_{2})

or P

_{A}= ρ

_{2}(dh + h

_{2}) - ρ

_{1}g (dh + h

_{1})

= dh [ρ

_{2}g - ρ

_{1}g] + h

_{2}ρ

_{2}g - h

_{1}ρ

_{1}g

But from equation(i) dh = a x h2 / A

P

_{A}= a x h

_{2}/ A [ρ

_{2}g - ρ

_{1}g] + h

_{2}ρ

_{2}g - h

_{1}ρ

_{1}g

As the area A is very large as compared to a, hence ratio a/A becomes very small and can be neglected. Then,

P

_{A}= h

_{2}ρ2 g - h

_{1}ρ

_{1}g

## (b) Inclined Single Column Manometer:

The inclined single column manometer or micro manometer with inclined tube. This manometer is more sensitive. Due to inclination the distance moved by the heavy liquid in the right limb will be more.Let L = Length of heavy liquid moved in right limb from X-X

θ = Inclination of right limb with horizontal

h

_{2}= Vertical rise of heavy liquid in right limb from X-X = Lx sin θ

For static equilibrium, the pressure at A is

P

_{A}= ρ

_{2}g h

_{2}- ρ

_{1}g h

_{1}

Substituting the valve of h

_{2}we get

P

_{A}= ρ

_{2}g L. sin θ - ρ

_{1 }g h

_{1}

For more help in

**Micromanometer**click the button below to submit your homework assignment