📘 fluid mechanics

1. **State the problem:** We have a pipe with diameter 300 mm (0.3 m) discharging water at 200 liters per second (0.2 m^3/s). Point 1 has pressure 260 kPa and point 2 is 3.4 m belo

1. The problem describes an inverted cone filled with fluid, with density $\rho = 1000$ kg/m³, gravitational acceleration $g = 9.8$ m/s², cone height $H = 2.5$ m, and top radius $R

1. **State the problem:** We are given the velocity distribution for flow over a plate as $$u=34y - y^2$$ where $$u$$ is velocity in m/s and $$y$$ is the distance in meters above t

1. **State the problem:** We want to find the pipe diameter needed to carry a discharge \(Q = 400\, \text{l/s} = 0.4\, \text{m}^3/\text{s}\) with an upstream head of at least 10 m

1. **Problem Statement:** We are given a circular arc surface AB with radius $r=2$ m and width into the paper of 1 m. The distance from the free surface of water to point E (bottom

1. **Stating the problem:** We have a surface AB which is a circular arc of radius $r=2$ m, width $w=1$ m (into the paper), with vertical distance from water surface E to B equal t

1. **Problem statement:** Find the magnitude and line of action of the hydrostatic force acting on surface AB, a circular arc with radius 2 m and width 1 m, submerged in water with

1. **Problem statement:** A 21-hp pump operates at 75% efficiency, drawing water from a 216 mm diameter suction pipe and discharging through a 148 mm diameter pipe where the veloci

1. **State the problem:** We have a cylindrical tank 14.59 m tall which empties completely in 10.20 minutes through a hole at the bottom. We want to find how long it takes for the

1. Stating the problem: Water flows into a motor through a pipe and exits through another pipe with given diameters, pressures, and a vertical height difference. We need to find th

1. The problem describes the steady motion of an incompressible viscous fluid between two parallel planes: the lower plane at rest (z = 0) and the upper plane moving with constant

1. **State the problem:** We need to find the gage pressure inside an air bubble of radius 1.0 mm (0.001 m) submerged 10 cm (0.1 m) below the free surface of water at 20°C. 2. **Un

1. Problem 1: Calculate viscosity of honey flowing through a capillary tube. Given:

1. **State the problem:** Calculate the mean velocity of olive oil flowing in a horizontal tube of diameter 0.0475 m where the pressure drop per meter is 1000 Pa. The oil viscosity

1. **State the problem:** We are given velocity components for an incompressible, steady flow with constant viscosity:\ $$u(y)=\frac{U}{h}y - \frac{hy}{2\mu}\frac{dp}{dx}\left(1-\f