Density Of Fluid Flowing Over Flat Plate Given Stanton Number Calculator

Formula Used:

\[ \rho_{fluid} = \frac{h_x}{St \cdot c \cdot u_{\infty}} \]

Local Heat Transfer Coefficient (hx):

W/m²·K

Stanton Number (St):

Specific Heat Capacity (c):

J/kg·K

Free Stream Velocity (u∞):

m/s

Density of Fluid (ρfluid):

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1. What is the Density Calculation Formula?

The formula calculates the density of fluid flowing over a flat plate using the Stanton number, local heat transfer coefficient, specific heat capacity, and free stream velocity. This relationship is derived from heat transfer principles in fluid dynamics.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \rho_{fluid} = \frac{h_x}{St \cdot c \cdot u_{\infty}} \]

Where:

\( \rho_{fluid} \) — Density of fluid (kg/m³)
\( h_x \) — Local heat transfer coefficient (W/m²·K)
\( St \) — Stanton Number (dimensionless)
\( c \) — Specific heat capacity (J/kg·K)
\( u_{\infty} \) — Free stream velocity (m/s)

Explanation: The formula relates fluid density to heat transfer characteristics and flow velocity, providing insight into fluid properties in convective heat transfer scenarios.

3. Importance of Fluid Density Calculation

Details: Accurate fluid density calculation is crucial for heat transfer analysis, fluid dynamics simulations, and designing thermal systems involving fluid flow over surfaces.

4. Using the Calculator

Tips: Enter all values in appropriate units. Ensure positive values for all inputs. The calculator provides density in kg/m³.

5. Frequently Asked Questions (FAQ)

Q1: What is the Stanton Number?
A: The Stanton Number is a dimensionless number that measures the ratio of heat transferred into a fluid to the thermal capacity of the fluid.

Q2: Why is free stream velocity important?
A: Free stream velocity affects the boundary layer development and heat transfer characteristics over the flat plate surface.

Q3: What are typical density values for common fluids?
A: Water: ~1000 kg/m³, Air: ~1.2 kg/m³, but density varies with temperature and pressure conditions.

Q4: When is this calculation most applicable?
A: This calculation is particularly useful for forced convection heat transfer analysis over flat plates in various engineering applications.

Q5: Are there limitations to this formula?
A: The formula assumes steady-state conditions and may have limitations for complex flow patterns or extreme temperature variations.