Understanding the fundamental formulas of Thermodynamics and Fluid Mechanics is essential for mastering core engineering principles.

 Understanding the fundamental formulas of Thermodynamics and Fluid Mechanics is essential for mastering core engineering principles. Here’s a quick, simplified breakdown 👇

⚙️ Thermodynamics Formulas:
1️⃣ First Law of Thermodynamics:
👉 Formula: Q = ΔU + W
✅ This law states that energy cannot be created or destroyed — it only changes form. The heat supplied to a system (Q) is used for increasing internal energy (ΔU) and performing work (W).
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2️⃣ Carnot Efficiency:
👉 Formula: η = 1 - (T_L / T_H)
✅ It represents the maximum efficiency of a heat engine operating between two temperature limits. Higher the temperature difference, higher the efficiency.
3️⃣ Polytropic Process Work:
👉 Formula: W = (P₂V₂ - P₁V₁) / (1 - n)
✅ Used to calculate work done when both pressure and volume change in a controlled process (like in compressors).
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4️⃣ Isothermal Process Work:
👉 Formula: W = P₁V₁ ln(V₂ / V₁)
✅ In an isothermal process, temperature remains constant. The work done depends on the volume ratio.
5️⃣ Adiabatic Process Equation:
👉 Formula: PV^γ = Constant
✅ No heat is exchanged with surroundings, typical in fast compression or expansion processes in engines.
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6️⃣ Internal Energy Change:
👉 Formula: ΔU = m c_v (T₂ - T₁)
✅ Represents the energy stored due to molecular motion inside a gas.
💨 Fluid Mechanics Formulas:
1️⃣ Density:
👉 Formula: ρ = m / V
✅ Describes how much mass is contained per unit volume — a key factor in fluid behavior.
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2️⃣ Pressure:
👉 Formula: P = F / A
✅ Defines the force acting per unit area. It’s the basic measure of fluid intensity.
3️⃣ Hydrostatic Pressure:
👉 Formula: P = ρgh
✅ Represents pressure exerted by a fluid column due to gravity and depth.
4️⃣ Head:
👉 Formula: H = P / (ρg)
✅ Shows the height of a fluid column that produces a given pressure.
5️⃣ Continuity Equation:
👉 Formula: A₁V₁ = A₂V₂
✅ States that mass flow rate is constant across a streamline — when pipe diameter decreases, velocity increases.
6️⃣ Bernoulli’s Equation:
👉 Formula: P + ½ρv² + ρgh = Constant
✅ Explains energy conservation in a flowing fluid — combining pressure, kinetic, and potential energy terms.
7️⃣ Reynolds Number:
👉 Formula: Re = ρvD / μ
✅ A dimensionless number that helps identify flow type — laminar or turbulent.