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Answer(s): H p atm p v . hill H. g end Air flows through the Venturi tube that discharges to the atmosphere as shown in the figure. If the flow rate is large enough, the pressure in the constriction will be low enough to draw the water up into the tube. Determine the flow rate, Q, needed to just draw the water into the tube.
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 ...
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.
A Bernoulli differential equation can be written in the following standard form: dy dx +P(x)y = Q(x)yn, 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 gives a differential equation in x and z that is linear, and can be solved using the integrating factor ...
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.
16 lis 2022 · Differential equations in this form are called Bernoulli Equations. First notice that if \(n = 0\) or \(n = 1\) then the equation is linear and we already know how to solve it in these cases. Therefore, in this section we’re going to be looking at solutions for values of \(n\) other than these two.
The Bernoulli equation is a mathematical statement of this principle. In fact, an alternate method of deriving the Bernoulli equation is to use the first and second laws of thermodynamics (the energy and entropy equations), ra-ther than Newton’s second law. With the approach restrictions, the general
