Solution Found!
(III) In Fig. 10-54, take into account the speed of the
Chapter 4, Problem 48P(choose chapter or problem)
(III) In Fig. , take into account the speed of the top surface of the tank and show that the speed of fluid leaving the opening at the bottom is
\(v_{1}=\sqrt{\frac{2 g h}{\left(1-A_{1}^{2} / A_{2}^{2}\right)}}\)
where \(h=y_{2}-y_{1}, \text { and } A_{1} \text { and } A_{2}\) are the areas of the opening and of the top surface, respectively. Assume \(A_{1} \ll A_{2}\) so that the flow remains nearly steady and laminar.
FIGURE 10-54 Problems 48 and 49
Equation Transcription:
Text Transcription:
v_1=\sqrt{\frac{2 g h(1-A_1^2 / A_2^2)
h=y_2-y_1, and A_1 and A_2
A_1 \ll A_2
Questions & Answers
QUESTION:
(III) In Fig. , take into account the speed of the top surface of the tank and show that the speed of fluid leaving the opening at the bottom is
\(v_{1}=\sqrt{\frac{2 g h}{\left(1-A_{1}^{2} / A_{2}^{2}\right)}}\)
where \(h=y_{2}-y_{1}, \text { and } A_{1} \text { and } A_{2}\) are the areas of the opening and of the top surface, respectively. Assume \(A_{1} \ll A_{2}\) so that the flow remains nearly steady and laminar.
FIGURE 10-54 Problems 48 and 49
Equation Transcription:
Text Transcription:
v_1=\sqrt{\frac{2 g h(1-A_1^2 / A_2^2)
h=y_2-y_1, and A_1 and A_2
A_1 \ll A_2
ANSWER:
Solution 48P:
We have to derive the equation of the velocity of water from the opening at the bottom of the container. This velocity of water is also known as velocity of efflux.
Step 1 of 4
Concept:
Continuity Principle: For the streamlined flow of water, the product of cross sectional area at any point to the velocity of water at that same point is always constant. Mathematically,
…(a)
Bernoulli’s Principle: The sum of the pressure energy, kinetic energy and potential energy for a streamlined system is always constant. Mathematically,
…(b)