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import streamlit as st |
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def main(): |
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st.title("Fluid Mechanics Concepts and Formulas") |
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st.sidebar.title("Navigation") |
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menu = ["Home", "Concepts", "Formulas"] |
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choice = st.sidebar.radio("Select a section:", menu) |
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if choice == "Home": |
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st.subheader("Welcome to the Fluid Mechanics App") |
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st.write(""" |
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This app provides key concepts and formulas for fluid mechanics. |
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Use the sidebar to navigate between different sections. |
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""") |
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elif choice == "Concepts": |
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st.subheader("Key Concepts in Fluid Mechanics") |
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st.write("### 1. Fluid Properties") |
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st.write("""- **Density (\(\rho\))**: Mass per unit volume. |
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\[\rho = \frac{m}{V}\] |
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- **Viscosity (\(\mu\))**: A measure of a fluid's resistance to deformation. |
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- **Pressure**: Force exerted per unit area. |
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""") |
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st.write("### 2. Flow Types") |
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st.write("""- **Laminar Flow**: Smooth, orderly flow. |
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- **Turbulent Flow**: Irregular, chaotic flow. |
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""") |
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st.write("### 3. Bernoulli's Principle") |
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st.write("""In a streamline flow, the total energy per unit volume remains constant: |
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\[P + \frac{1}{2}\rho v^2 + \rho gh = \text{constant}\] |
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""") |
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elif choice == "Formulas": |
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st.subheader("Fluid Mechanics Formulas") |
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st.write("### 1. Continuity Equation") |
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st.latex(r"A_1 v_1 = A_2 v_2") |
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st.write("""The product of cross-sectional area and velocity is constant for an incompressible fluid. |
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""") |
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st.write("### 2. Bernoulli's Equation") |
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st.latex(r"P + \frac{1}{2}\rho v^2 + \rho gh = \text{constant}") |
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st.write("""Relates pressure, velocity, and height in a flowing fluid. |
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""") |
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st.write("### 3. Reynolds Number") |
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st.latex(r"Re = \frac{\rho v D}{\mu}") |
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st.write("""Determines whether flow is laminar or turbulent. |
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""") |
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st.write("### 4. Hydrostatic Pressure") |
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st.latex(r"P = \rho g h") |
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st.write("""Pressure at a depth \(h\) in a fluid of density \(\rho\). |
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""") |
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if __name__ == '__main__': |
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main() |
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