The pressure at a point in the fluid is 4.9 N/cm2. Find height when th...
Given Data:
Pressure at a point in the fluid = 4.9 N/cm²
Specific gravity of oil = 0.85
Formula:
The pressure at a point in a fluid can be calculated using the formula:
Pressure = ρgh
where,
ρ = density of the fluid
g = acceleration due to gravity
h = height of the fluid column
The density of the fluid can be calculated using the formula:
ρ = specific gravity × density of water
Calculation:
Given that the specific gravity of the oil is 0.85. The density of water is 1000 kg/m³.
Step 1: Calculate the density of the oil:
Density of oil = specific gravity × density of water
Density of oil = 0.85 × 1000 kg/m³
Density of oil = 850 kg/m³
Step 2: Convert the pressure units:
Given pressure = 4.9 N/cm²
1 N/cm² = 1 N/(0.01 m)² = 10000 N/m²
Pressure = 4.9 × 10000 N/m²
Pressure = 49000 N/m²
Step 3: Rearrange the formula and solve for height:
Pressure = ρgh
h = Pressure / (ρg)
h = 49000 N/m² / (850 kg/m³ × 9.81 m/s²)
h ≈ 5.81 m
Therefore, the height of the fluid column is approximately 5.81 meters.
Final Answer:
The height of the fluid column when the pressure at a point in the fluid is 4.9 N/cm² and the fluid is oil with a specific gravity of 0.85 is approximately 5.81 meters.