An inclined manometer is a useful device for measuring small pressure differences. 

The formula given in Section 3.4 for the pressure difference in terms of the liquid-level difference h remains valid, but while h would be small and difficult to read for a small pressure drop if the manometer were vertical, L can be made quite large for the same pressure drop by making the angle of the inclination, θ, small. 

(a) Derive a formula for h in terms of L and θ. 

(b) Suppose the manometer fluid is water, the process fluid is a gas, the inclination of the manometer is θ = 15°, and a reading L = 8.7 cm is obtained. What is the pressure difference between points 1 and 2 ? 

(c) The formula you derived in Part (a) would not work if the process fluid were a liquid instead of a gas. Give one definite reason and another possible reason. 

Formula in section 3.4 

P₁ + ρ₁gd₁ = P₂ + ρ₂gd₂ + ρfgh

P₁ - P₂ = (ρ_f - ρ)gh 

h