5th semester files

5th-Semester-Fall-2023/ME-For-ECEs/Notes/Fluids.md

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+# Fluid Mechanics
+
+##### Density
+$$\rho = {m \over V}$$
+
+##### Specific weight
+$$\gamma = {m g \over V} = \rho V$$
+
+##### Viscosity
+- Resistance to flow
+- Ability to resist shear force
+
+### Example
+Consider a fluid between two plates a distance, $b$, apart. One is moving with velocity, $\vec{u}$, and the other is fixed in place. The moving plate applies a force, $\vec{p}$ to the fluid. The fluid has continuously changing velocity between the two plates.
+
+The velocity gradient between the two plates is given by:
+$${du \over dy}$$
+
+The shearing stress, $T$, is given by:
+$$\vec{T} = {\vec{p} \over A} = \mu {du \over dy}$$
+
+Where $\mu$ is the absolute viscosity.
+
+### Pressure in a Fluid
+$$p_2 = p_1 + \rho g z$$
+
+##### Pascal's Law
+$${F_1 \over A_1} = {F_2 \over A_2}$$
+
+##### Archemedes Principle
+The upward force of bouyancy, $F_B$, is given by the weight of the displaced fluid.
+
+### Continuity Equation
+$$A_1 \vec{v}_1 \Delta t = A_2 \vec{v}_2 \Delta t$$
+
+Conservation of mass principle applied to a steady flow. The mass flow rate $\dot{m}$ is given by:
+$$\dot{m} = \rho_1 A_1 \vec{v}_1 = \rho_2 A_2 \vec{v}_2$$
+
+Flowrate:
+$$\vec{Q} = A \vec{v}$$
+
+### Bernoulli's Equation
+$$p_1 + {1\over2}\rho v_1^2 + \rho g h_1 = p_2 + {1\over2}\rho v_2^2 + \rho g h_2$$
+
+An increase in speed of a fluid occurs with a decrease of static pressure or decrease in potential energy.