Water is used as the manometric liquid in a pitot tube mounted in an aircraft to measure air speed. If the maximum difference in height between the liquid columns is 0.1 m, the maximum air speed that can be measured is 5z m/s (nearly). Find z. Density of air dₐᵢᵣ=1.3 kg/m³; (g=10 m/s²)
Physics · Mixed Chapter
JEE Mains

Question

Water is used as the manometric liquid in a pitot tube mounted in an aircraft to measure air speed. If the maximum difference in height between the liquid columns is 0.1 m, the maximum air speed that can be measured is 5z m/s (nearly). Find z. Density of air dₐᵢᵣ=1.3 kg/m³; (g=10 m/s²)

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: The pressure difference in a Pitot tube is the air dynamic pressure Δp=½ρₐᵢᵣ v². Step 2: Manometer reading h=0.1 m corresponds approximately to Δp=(density of water−ρₐᵢᵣ)gh≈(1000−1.3)×10×0.1≈998.7 Pa. Step 3: Equating ½(1.3)v²≈998.7 yields v≈√(1997.4/1.3)≈39.2 m/s. Step 4: Given v≈5z m/s, z≈39.2/5≈7.84, nearest integer z=8.