📘 fluid mechanics

1. **Stating the problem:** Given the Reynolds number $Re = 8.8 \times 10^{4}$, find the frictional factor $f$. 2. **Formula and explanation:** For turbulent flow in smooth pipes,

1. **Problem statement:** Calculate the power required to pump aqueous nitric acid through a steel pipe, the gauge pressure at the pump outlet, and the effects of increased pipe ro

1. **Problem Statement:** A Venturimeter has an entrance diameter $d_1 = 0.3$ m and a throat diameter $d_2 = 0.2$ m. The discharge coefficient $C_d = 0.96$. The specific weight of

1. **Problem Statement:** Find a formula for the flow rate $\alpha$ of a fluid through a pipe in terms of fluid viscosity $\eta$, pressure gradient per unit length $\frac{\Delta P}

1. Statement of the problem. Find the center of pressure of a vertical rectangular gate of width $b=3$ m and height $h=7$ m whose top edge is at depth $y_{top}=2.5$ m below the fre

1. **Problem Statement:** Calculate the buoyant force and the center of pressure on a vertical rectangular surface submerged in water. 2. **Given:**

1. **Problem statement:** Calculate the buoyant force acting on a rectangular vertical surface submerged in water. The surface dimensions are 3 m by 7 m, and the top of the surface

1. **Problem statement:** Water flows through a cylindrical pipe with a radius of 1.5 cm at a speed of 9 cm/s. We need to find the volume of water flowing through the pipe in 1 hou

1. **بيان المشكلة:** لدينا حديقة عامة تحتوي على 15 شجرة صغيرة كل واحدة تحتاج 4 لترات/ساعة × 2 منقطات، و25 شجيرة كل واحدة تحتاج 4 لترات/ساعة × 1 منقط.

1. The problem asks: What is a fluid column? 2. A fluid column is a vertical section of fluid contained between two surfaces, typically between the bottom and the top of a fluid bo

1. **Stating the problem:** We want to understand and use the formulas related to relative density (specific gravity), density, pressure, and head in fluid mechanics.

1. **State the problem:** We have a venturimeter installed in a pipeline of diameter $D_1 = 100$ mm carrying oil with specific gravity $SG = 0.87$. The maximum differential gauge r

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