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Sample Problem 1: Solve the differential equation y0−2ty= 2ty2. Solution: This is a Bernoulli equation with r= 2. Hence 1 −r= −1 and the function z= y−1 solves the equation z0+ 2tz= −2t. To find z, we use the method of variation of the unknown constant (the Lagrange method): z= Ce−t2 −e−t2 Z 2te t2 dt= Ce−t2 −e−2 Z sesds ...
Microsoft Word - Bernoulli_PracticeProblems. Water is siphoned from a large tank through a constant diameter hose as shown in the figure. Determine the maximum height of the hill, Hhill, over which the water can be siphoned without cavitation occurring.
Problem 1. Water is flowing in a fire hose with a velocity of 1.0 m/s and a pressure of 200000 Pa. At the nozzle the pressure decreases to atmospheric pressure (101300 Pa), there is no change in height. Use the Bernoulli equation to calculate the velocity of the water exiting the nozzle.
Worked Example Problems: Bernoulli’s Equation P1 ˆg +z 1 + V2 1 2g = P2 ˆg +z 2 + V2 2 2g The objective in all three of the following worked example problems is to determine the pressure at location 2, P 2. For all three problems the gravita-tional constant, g, can be assumed to be 9:81m=s2 and the density of water, ˆ, as 1000kg=m3. All ...
3.3 Rozkład Bernoulliego - zadania. Kurs “Statystyka na skróty” - Cyrkiel.info. 3.3 Rozkład Bernoulliego - zadania. Kurs “Statystyka na skróty” - Cyrkiel.info. Pewien wtašciciel ma 5 stoisk z kosmetykami podobnej wielkoéci na bazarach. Pr-stwo, Že stoisko bedzie zyskowne danego dnia wynosi 0.8. Obliczyé pr-stwo, Že a) tylko ...
Bernoulli differential equation can be written in the following standard form: dy. + P(x)y = Q(x)yn , dx where n 6= 1 (the equation is thus nonlinear). To find the solution, change the dependent variable from y to z, where. z = y1−n.
This document contains the answers to two practice problems applying the Bernoulli equation. The first problem calculates the velocity of water exiting a fire hose nozzle given the inlet velocity and pressures.
