📘 fluid mechanics

### Problem 1: Vertical trapezoidal gate under water pressure 1. **Problem statement:**

### Problem 1: Vertical trapezoidal gate under water pressure 1. **Problem statement:**

1. **Problem Statement:** We need to find the angle $\theta$ of the tube given the pressure difference $P_1 - P_2 = 8500$ Pa (converted from kPa) and the tube length $L = 0.25$ m (

1. **Problem Statement:** Water flows through a Venturi meter with flow rate $Q = 2$ m$^3$/s. The inlet diameter is $D_1 = 0.8$ m. Mercury manometer shows a height difference $h =

1. **Problem statement:** Water leaves the impeller of a centrifugal pump with velocity $$v_{rel} = 25\ \text{m/s}$$ and acceleration $$a_{rel} = 30\ \text{m/s}^2$$ relative to the

1. **State the problem:** We need to find the rate of increase in the mass of the cylinder, given two supply pipes feeding gas and water, and an outlet valve delivering gas at a ce

1. El problema consiste en entender las ecuaciones de Navier-Stokes, que describen el movimiento de fluidos. 2. Las ecuaciones de Navier-Stokes para un fluido incompresible y visco

1. **Planteamiento del problema:** Calcular la presión manométrica en PSI del aire dentro del tanque usando las alturas y densidades dadas.

1. The problem involves understanding the relationship between flow rate and volume. 2. Given flow rate $Q = 11.9$ m³/s and total volume $V = 67205600$ m³, we want to find the time

1. **Problem statement:** Calculate the height difference $h$ in a manometer connected to a pipe where fluid flows at velocity $v = 2.0$ m/s.

1. **State the problem:** Convert the given pressure readings to kPa absolute, assuming the barometer reads 29.92 in. Hg (which is standard atmospheric pressure). 2. **Important fo

1. The problem asks about the meaning of "tank is situated at height of 20 m from water level." 2. This means the bottom or base of the tank is located 20 meters above the water su

1. **Stating the problem:** We are given a set of mathematical expressions describing a flow domain with variables $a_1$, $b$, $v$, $\phi$, $f$, velocity $\mathbf{v}$, and geometri

1. **Problem Statement:** You asked to solve a problem using Bernoulli's equation. Bernoulli's equation relates pressure, velocity, and height in fluid flow along a streamline.

1. The problem is to compute the efficiency of a centrifugal blower. 2. Efficiency ($\eta$) of a centrifugal blower is defined as the ratio of the useful power output to the power

1. **Stating the problem:** Given pressures $p_1 = 9.16$, $p_2 = 2.19$, $p_3 = 1.19$ and distances $a = 19.2$, $b = 4.65$, $c = 4.05$, $d = 3.26$, $e = 3.82$, we want to analyze th

1. **State the problem:** A fire engine pumps water with a velocity of $15\ \text{m/s}$ hitting a wall perpendicularly and sticking to it. We need to calculate the pressure exerted

1. The problem is to understand and use the Hazen-Williams formula, which is commonly used in hydraulics to estimate the pressure drop or flow rate in pipes due to friction. 2. The

1. The problem is to solve the Hazen-Williams equation, which is used to calculate the pressure drop or head loss due to friction in a pipe carrying water. 2. The Hazen-Williams eq

1. مسئله: در یک لوله افقی با جریان لایه‌ای و یکنواخت، سرعت جریان در قسمتی از مسیر 75 درصد تغییر می‌کند و فشار افزایش می‌یابد. باید درصد تغییر قطر لوله را پیدا کنیم. 2. فرمول اصلی:

1. مسئله: فشار پیمانه‌ای گاز درون مخزن را پیدا کنیم که در لوله U شکل، روغن و آب هم‌ارتفاع هستند. 2. داده‌ها: