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Fluid Mechanics in Engineering
Pressure, Flow Rate, Viscosity, and Turbulence
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Fluid mechanics explains how liquids and gases move and how they push on surfaces. Engineers use it to design pipes, pumps, aircraft, hydraulic systems, and medical devices. Three core ideas are pressure, flow rate, and viscosity. Together they determine how easily a fluid moves and how much energy is needed to transport it.
When fluid travels through a pipe, its speed can change if the pipe diameter changes. In narrower sections, the fluid usually moves faster, and pressure often drops along the flow because energy is lost to friction and viscous effects. Viscosity measures a fluid's internal resistance to motion, which creates a boundary layer near solid walls where the fluid speed is reduced. These ideas are connected by continuity, Bernoulli's principle, and flow resistance relations such as Poiseuille's law.
Key Facts
- Pressure is force per area: P = F/A
- Volumetric flow rate is Q = A v for steady incompressible flow
- Continuity in a pipe gives A1 v1 = A2 v2
- Bernoulli equation along a streamline: P + 1/2 rho v^2 + rho g h = constant
- For laminar flow in a circular pipe, Poiseuille's law is Q = (pi r^4 Delta P)/(8 eta L)
- Reynolds number predicts flow regime: Re = rho v D / eta
Vocabulary
- Pressure
- Pressure is the normal force exerted by a fluid per unit area on a surface.
- Flow rate
- Flow rate is the volume of fluid passing a point each second.
- Viscosity
- Viscosity is a measure of how strongly a fluid resists deformation and flow.
- Boundary layer
- The boundary layer is the thin region near a wall where fluid velocity changes from zero at the surface to the main flow speed.
- Laminar flow
- Laminar flow is smooth fluid motion in parallel layers with little mixing between them.
Common Mistakes to Avoid
- Assuming pressure is always higher where velocity is higher, which is wrong because in many steady pipe and streamline situations higher speed corresponds to lower static pressure.
- Using Q = A v with inconsistent units, which is wrong because area must be in m^2 and velocity in m/s to get flow rate in m^3/s.
- Treating viscosity and density as the same property, which is wrong because density measures mass per volume while viscosity measures resistance to flow.
- Applying Bernoulli's equation without considering friction losses, which is wrong because real fluids in pipes lose mechanical energy due to viscosity and wall drag.
Practice Questions
- 1 Water flows steadily through a horizontal pipe. The pipe diameter decreases from 0.10 m to 0.050 m. If the speed in the wide section is 2.0 m/s, what is the speed in the narrow section?
- 2 Oil with viscosity eta = 0.20 Pa s flows laminarly through a pipe of radius 0.010 m and length 2.0 m. If the pressure drop is 5000 Pa, use Q = (pi r^4 Delta P)/(8 eta L) to find the volume flow rate.
- 3 Two fluids move through identical horizontal pipes at the same average speed. One fluid has much higher viscosity than the other. Explain which fluid will have the larger pressure drop over the same pipe length and why.