**Educational Content: Water Flow Analysis in an Open Tank****Problem Statement:**The open tank contains water at 20 °C and is being filled through section 1. Assume incompressible flow. 1. Derive an analytical expression for the rate of change of the water level, \( \frac{dh}{dt} \), in terms of arbitrary volume flows (\( Q_1, Q_2, Q_3 \)) and tank diameter \( d \).2. If the water level \( h \) is constant, determine the exit velocity \( v_2 \) using the given data: - \( v_1 = 3 \, \text{m/s} \) - \( Q_3 = 0.01 \, \text{m}^3/\text{s} \) - Given diameter \( d = 50 \, \text{cm} \).**Diagram Explanation:**- The diagram shows a vertical open tank with a water inflow at section 1 (left side), an outflow at section 2 (right side), and an additional outflow marked as section 3 (top).- Inflow at section 1 has a diameter \( D_1 = 5 \, \text{cm} \).- Outflow at section 2 has a diameter \( D_2 = 7 \, \text{cm} \).- The top outflow, marked as section 3, has a fixed flow rate \( Q_3 = 0.01 \, \text{m}^3/\text{s} \).- The tank diameter \( d \) is given as 50 cm.**Select the correct exit velocity \( v_2 \) from the options:**- \( 5.38 \, \text{m/s} \)- \( 3.42 \, \text{m/s} \)- \( 2.56 \, \text{m/s} \)- \( 4.13 \, \text{m/s} \)**Solution Approaches:**To solve this problem, apply the continuity equation for incompressible fluid flow, and consider the conservation of mass in the system. By maintaining the water level constant (\( \frac{dh}{dt} = 0 \)), you equate the inflows and outflows to solve for \( v_2 \).

Flow incompressibleFlow Q1 and Q3 are entering the tank and flow Q2 is exiting the tankInlet…

The open tank contains water at 20 °C and is being filled through section 1. Assume incompressible flow. First derive an analytical expression for the water-level change dh/dt in terms of arbitrary volume flows (Q1, Q2, Q3) and tank diameter. Then, if the water level h is constant, determine the exit velocity v2 for the given data v1 = 3 m/s and Q3 = 0.01 m3/s. Given that d = 50 cm. D₁ = 5 cm 3 Q = 0.01 m³/s h Water D₂=7 cm

The open tank contains water at 20 °C and is being filled through section 1. Assume incompressible flow. First derive an analytical expression for the water-level change dh/dt in terms of arbitrary volume flows (Q1, Q2, Q3) and tank diameter. Then, if the water level h is constant, determine the exit velocity v2 for the given data v1 = 3 m/s and Q3 = 0.01 m3/s. Given that d = 50 cm. D₁ = 5 cm 3 Q = 0.01 m³/s h Water D₂=7 cm

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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