Intro to Fluid Mechanics for Engineering Students Part 2

Explore conservation of mass with control volumes and velocity profiles. Define volumetric flow, mass flow rate, and average velocity; compute q and m dot via area and dot product.

Compute the inlet velocity and mass flow for a 1-by-5-inch vacuum inlet by converting 25 ft³/min to m³/s and using sea level density in a one-dimensional flow.

Compute mass flow rate for a nonuniform, truncated conical velocity profile in a circular pipe using cone volume and similar triangles to find Q, then multiply by density 880 kg/m³.

Study finite control volumes, control surfaces, and open and closed portions, applying outward normal direction and sign conventions for inflow and outflow, including fixed, moving, and changing shapes.

Calculate inlet A and outlet B velocities from a fixed volumetric flow rate using cross-sectional areas and dot product, within a control-volume framework.

Understand the Reynolds transport theorem and how it converts conservation laws from a Lagrangian to an Eulerian control-volume view, using extensive and intensive properties.

Analyze air flow through a duct using a control volume with inlet and outlet. Assume incompressible air with constant density and apply Reynolds transport theorem to local and convective changes.

demonstrate a moving control volume around a water jet, define open surfaces and relative inlet and outlet velocities, explain incompressible flow, and why motion clarifies local and convective changes.

Outline a control volume around a hemispherical bowl fed by a water jet, identify inlet and outlet, apply Reynolds transport theorem, and note convective changes for incompressible, steady flow.

explains conservation of mass via the reynolds transport theorem and a control volume, deriving the continuity equation and mass flow concepts for incompressible, steady flow.

Compute the acceleration a(x) of water in a converging nozzle using the continuity equation and velocity-times-area relation; derive v(x) from Q and A(x), yielding a(x) = 1.5e-4/(π^2(0.025-0.1875x)^5).

Apply the continuity equation to a multiport pipe network with incompressible water, and balance mass at inlets A and C and outlet B to solve for velocity at C.

Apply conservation of mass to a six-nozzle coating problem, determine the strip speed required to produce a 1 mm coating by balancing nozzle volumetric flow with the moving strip area.

Apply the continuity equation to an incompressible two-inlet tank to derive the rate at which the water level rises, using inlet flows, area, and volume changes.

Apply conservation of mass to a deforming control volume as a plunger moves, relating syringe volume change to the needle outlet velocity of an incompressible fluid.

This lecture derives Euler's equations of motion for an inviscid, steady flow along a streamline, introducing tangential and normal accelerations, the Bernoulli equation, and pressure-weight forces.

Analyze steady horizontal flow of an ideal, inviscid, incompressible fluid in open and closed conduits, showing PB = PA and PC = PA + rho g h.

Analyze air flow through a horizontal tapered duct at 20°C to compute the acceleration along a streamline from 101.3 kPa to 100.6 kPa, using density 1.202 kg/m³, assuming constant density.

Determine the average change in pressure along a horizontal streamline for water with 15 m/s^2 acceleration in a converging nozzle, yielding delta p equals -12 kPa.

Explain pressure variation in a horizontal pipe bend for an ideal fluid with density rho and velocity v; derive delta p = rho v^2 ln(r/rI) using the normal direction equation.

Derive and apply Bernoulli's equation from Euler's equations for steady, inviscid, incompressible flow along a streamline, linking pressure, velocity, and elevation via p/rho, v^2/2, and gz, and noting limitations.

apply bernoulli and continuity to determine mass flow in a duct with a 400 mm to 200 mm reducer, assuming incompressible air at 20°C and density 1.202 kg/m³.

Apply Bernoulli and continuity to a 100 mm to 20 mm water pipe, solving for pressure and velocity at C, given A is 120 kPa and B is 12 m/s.

Compute the funnel discharge by applying Bernoulli and continuity, deriving velocity from energy balance and cone geometry, then determine Q at the outlet.

Derive and apply the linear momentum equation using the Reynolds transport theorem to relate forces, momentum change, and convection in a control volume for steady, ideal fluid flow.

Apply the linear momentum equation to a horizontal oil flow in a 100 mm pipe elbow to determine the x and y force components from inlet and outlet conditions.

Finds horizontal and vertical forces at A for a 40 mm pipe with 0.015 m^3/s flow, using Bernoulli and momentum to get ax = 0 and ay = -294.56 N.

Analyze a two-diameter pipe with a seam to determine the horizontal shear force at C using continuity, Bernoulli's equation, and linear momentum, given 65 kPa at A.

Analyze constant-velocity fluid interactions using relative velocity and a moving control volume. Apply the convective term to relate the fluid velocity to blade velocity and analyze inlet–outlet momentum.

Compute the horizontal force on a moving blade deflecting water using a relative velocity control volume and the linear momentum equation for an ideal steady flow.

Compute the power produced by a water stream striking a moving cart with a moving control volume, using the linear momentum equation and the relative velocity to determine the result.

Apply the relative velocity and momentum balance within a moving control volume to compute the blade force from a deflected jet flow, including velocity components and volumetric flow rate.

Apply the angular momentum equation via the Reynolds transport theorem to compute torque from fluid flow around a fixed axis, using r cross mv and control-volume angular momentum changes.

Using the angular momentum equation, a four-nozzle sprinkler's torque is computed by splitting Q among arms, finding exit velocity, and summing moments about the z-axis to yield 46.5 N·m.

Explore fluid mechanics of a 200 mm pipe bend: compute axial and vertical forces, moment, and flow rate using Bernoulli and momentum analyses.

Determine the horizontal and vertical forces at the fixed support and the moment for pipe equilibrium, using continuity and Bernoulli for discharge at 10 m/s.