Inclined manometer - complete PDF

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Download Inclined manometer - complete PDF

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 One disadvantage of the U-tube manometer is that liquid movement in both limbs must be read. However, if one limb is made much wider than the other, liquid movement in that limb will be much smaller than that in the narrower limb. A pressure measurement with only a small error can be made by reading the liquid level in the narrow limb only. Additionally, the narrow limb may be inclined. This amplifies liquid movement in the limb, allowing more accurate measurements, and is useful for measuring small pressure differences.

A pressure difference is applied and causes liquid in the narrow limb to rise a vertical distance, z. But the movement measured is x (larger). Liquid in the wide limb drops a distance, h (small). volume lost in wide limb = volume gained in narrow limb 2

2

D d π   h = π  x 2  2



d h = x   D

2

Consider level A – B. For wide limb:

p A = p1 + ρgH + ρgh

For narrow limb:

p B = p2 + ρ m gz + ρ m gh

(1)

Since

pA = pB p1 + ρgH + ρgh = p2 + ρ m gz + ρ m gh

The required pressure difference is p1 − p 2 = ρ m gz + ρ m gh − ρgH − ρgh

= ρ m g (z + h) − ρ g (H + h) 2 2   d  d   = ρ m g z + x   − ρ g  H + x    D    D    

2   d   gx = ρ m sin θ +    − ρ g  H +  D    

d  x  D

using (1)

2

  

since z = x sin θ

If D is large compared to d, p1 − p 2 ≈ ρ m gx sin θ − ρ gH

ie, an approximate value of pressure difference is obtained using narrow limb measurement only....