Intro to Fluid Mechanics for Engineering Students Part 1

Pressure is the normal force per unit area in a fluid at rest, with no shear, and Pascal's law shows this pressure is the same in all directions.

Define absolute, gauge, and atmospheric pressures; explain zero absolute pressure in a vacuum, standard atmospheric values, and how p abs = p atm + p g links the concepts.

Explore how pressure varies with depth in a static hydrostatic fluid, show horizontal pressure remains constant, and derive dP/dz = -gamma to explain higher bottom pressure.

Derive p = p0 + gamma h for incompressible fluids with downward z, and define gauge pressure and pressure head as the height of a liquid column, P/gamma.

Determine the mercury pressure head from a 40 kilopascal gauge pressure using absolute and atmospheric pressures, yielding a 301 mm mercury column.

Calculate the tank bottom pressure with hydrostatic balance, accounting for 65 kPa trapped air and water weight. Determine the standpipe rise h using p0 plus gamma h and gauge pressure.

Explore a 0.2 mm bubble in carbonated water at 10 C and 101 kPa, using an ideal gas model to find the bubble diameter at the surface.

Derive how pressure varies in compressible fluids using the ideal gas law, and apply isothermal formulas to atmospheric layers from sea level to the lower stratosphere.

Analyze hydrostatic pressure in a compressible liquid with density varying as rho = 1.75 h + 825, and compute the gauge pressure at h = 25 m, about 207.7 kPa.

Discover how a mercury barometer measures atmospheric, or absolute, pressure by inverting a mercury-filled tube in a bath, with the column height in millimeters of mercury indicating pressure.

Learn how manometers measure pressure differences using hydrostatic equation with two-fluid columns, and relate heights to pressure via p2 minus p1 equals minus gamma h, where gamma equals rho g.

Calculate the gauge pressure in a closed tank by applying the hydrostatic equation with oil (SG 0.9) and mercury (SG 13.6), converting gamma values, and tracing pressure around points.

Analyze a multi-fluid manometer problem to determine pressure difference using hydrostatic equations, convert gamma values, reference line, and balances across water, mercury, and oil, yielding pa minus pb 3.74 psi.

Apply the hydrostatic equation to compute the pressure in a water mercury pipe, using gamma values and densities to find the gauge pressure at point a.

Solve an inclined oil–mercury manometer to determine the pressure difference between A and B, calculating gamma and applying vertical distances and a reference line to get 20.11 kPa.

Explore hydrostatic forces on plane submerged surfaces with fluids at rest, derive the resultant force and its line of action, and how pressure variation yields FR perpendicular to the surface.

Locate the center of pressure y_p for the resultant hydrostatic force on an inclined submerged area using moments, I_x, y_bar, h_bar, and parallel axis theorem.

Derive xp by equating pressure moments to force moments, yielding xp as ratio of integral xy da to integral y da, with symmetry placing p on centroidal y axis.

Calculate the resultant hydrostatic force on a rectangular gate immersed in oil and determine its center of pressure using centroid, h-bar, gamma, and the contact area.

Compute the hydrostatic force on a rectangular gate using centroid and h-bar. Apply a moment equilibrium about the hinge to determine the required perpendicular force P.

Compute the water pressure on a hinged rectangular gate and determine the required depth h using the specific weight 62.4 lb/ft^3, the resultant force, the centroid, and the moment balance.

Analyze hydrostatic forces on a submerged car door by computing outside and inside resultant pressures, then apply a hinge-based moment to determine the hand force required.

Explore a geometric method for hydrostatic force on a plane surface using the pressure prism, converting p da to dv and locating resultant through centroid of the pressure prism.

Determine dam thickness b to prevent overturning under water pressure, using a 1 m width and densities 2.4e3 and 1000 kg/m^3, by moment balance to get b ≈ 3.56 m.

Determine the maximum water depth that causes a submerged gate to verge on opening by analyzing hydrostatic pressures, gate weight, and moments with a free-body diagram.

Explore hydrostatic forces on curved surfaces by analyzing horizontal and vertical projections, computing FH and FV, and applying centroid and equilibrium concepts.

Calculate horizontal and vertical forces on a curved panel by using vertical and horizontal projections, gamma, and h_c, yielding about 706 kN horizontal and 639 kN vertical.

Calculate the horizontal and vertical hydrostatic forces on a 50 m wide quarter-circle dam and locate the center of pressure for the resultant.

Compute horizontal and vertical reactions at pin B for a parabolic and flat plate submerged in water, using hydrostatic pressure on projected areas and moment balance.

Define buoyancy for submerged and floating bodies by equating buoyant force to displaced fluid weight; floating bodies displace fluid equal to their own weight.

Explore how buoyant force from seawater reduces crane tension when lifting a concrete block. The example contrasts air and water conditions, using volume and densities to compute tension.

Apply buoyant force equals weight to relate the block’s displaced volume to its weight, then use volume balance to find the final height h.

Compute the sphere’s weight by equating it to buoyant force via displaced volume; determine the specific gravity, then assess flotation in gasoline and the exposed volume.

Compute the buoyant force and string tension for a five-meter wooden rod with four meters submerged, then determine the wood’s specific gravity from weight and buoyancy using a free-body diagram.

Explore buoyancy and stability of floating bodies by comparing the center of gravity and center of buoyancy, and using the metacentre to assess stable, unstable, or neutral equilibrium.

Determine if a wooden cylinder floats stably in oil (SG 0.85) by calculating submerged length and using buoyancy and force balance with centers of gravity, buoyancy, and metacenter.

Explore how horizontal and vertical accelerations alter liquid pressure, derive the tilt angle theta, and compare open and closed containers using p equals gamma h.

Analyze a decelerating truck water tank to determine the surface inclination angle theta using tan theta = a/g, then compute bottom pressures at A and B.

Determine pressure at point B for the rail car at rest and under a 3 m/s^2 leftward acceleration, and compute water spilled (32 m^3 to 28.43 m^3, 3.57 m^3).

A rotating liquid forms a paraboloid surface. Pressure rises with radius: ∂p/∂r = γ ω^2 r / g, and h = ω^2 R^2 /(2 g).

Determine the angular velocity needed to just expose the tank bottom as water forms a paraboloid surface, by conserving volume and solving for omega.