Question

The inclined-tube manometer shown has D = 110 mm and d = 8.0 mm. (a) Determine the angle, θ, required to provide a 5 : 1 increase in liquid deflection, L, compared with the total deflection in a regular U-tube manometer. (b) Evaluate the sensitivity of this inclined-tube manometer. Assume that manometer is filled with Meriam red oil. Use Table A.1

Answer 1

By continuity equation;

$x A_{tank} = LA_{tube}$

$\Rightarrow x(\pi/4)D^2= L(\pi/4)(d)^2$

$\Rightarrow x= L \left ( \frac{d}{D} \right )^2$

For a U shaped manometer;

$\Delta P = \rho g h$

For inclined manometer;

$\Delta P = \rho g (x +Lsin\theta)$

Equating both pressures;

$\Rightarrow \rho g h = \rho g (x +Lsin\theta)$

$\Rightarrow h = (x +Lsin\theta)$

$\Rightarrow h =L \left ( \frac{d}{D} \right )^2 +Lsin\theta$

$\Rightarrow 1=\left (\frac{L}{h} \right )\left [ \left ( \frac{d}{D} \right )^2 +sin\theta \right ]$

$\Rightarrow 1=\left (\frac{5}{1} \right )\left [ \left ( \frac{8}{110} \right )^2 +sin\theta \right ]$

$\Rightarrow \theta = 11.23^o$

...(Answer)

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For Meriam Red Oil (Using Table A-1);

$\fn_jvn (SG) = 0.827$

Sensitivity is given as;

$s = \frac{L}{h(SG)}$

$\fn_jvn \Rightarrow s = \frac{5}{0.827}$

$\fn_jvn \Rightarrow s = 6.046$

...(Answer)