An inviscid fluid with density, ρ, discharges into the atmosphere through the device shown below. The height differences between the inlets and outlets are appreciable but unknown. Determine the horizontal component of force at the flange required to hold the device in place in terms of A1, V1, θ, and p. **Fluid Dynamics and Force Components in Fluid Mechanics**In fluid mechanics, the study of forces acting on fluids in motion is essential. Consider a device through which an inertial fluid of density \(\rho\) discharges into the atmosphere. The setup comprises various significant aspects that influence the behavior of the fluid and forces involved. Understanding these elements enables us to determine the horizontal component of force at specific points within the system.### Diagram Analysis**System Description:**The diagram illustrates a pipe system where a fluid flows from an inlet at the left and discharges at an outlet to the atmosphere at the right. **Key Elements:**- **Inlet (Section 1):** - **Area (A\[1\]), Velocity (V\[1\])**: Initially, the fluid enters through an inlet section of area \(A\[1\]\) with velocity \(V\[1\]\).- **Flange:** A pressure gauge is depicted near the flange, indicating a fluid pressure \(P_1 = 1.5 \times 10^6\) Pa. - **Outlet (Section 2):** - **Area (A\[2\]), Velocity (V\[2\])**The fluid exits through an outlet section of area \(A\[2\]\), with a given relation \(A_2 = 0.5A_1\), indicating that the outlet area is half the inlet area.### Problem Statement:Given that the height differences between the inlet and outlet are appreciable but unknown, determine the horizontal component of force at the flange required to hold the device in place. Express this in terms of \(A\[1\], V\[1\], \theta,\) and \(\rho\).**Methodology:**1. **Continuity Equation:** Since the mass flow rate must be constant, apply the continuity equation: \[ A\[1\]V\[1\] = A\[2\]V\[2\] \]2. **Bernoulli’s Equation:** Apply Bernoulli’s principle between the inlet and outlet.3. **Force Calculation:** Use the momentum equation in the horizontal direction to derive the expression for the force component. ### Conclusion:By understanding these relationships and principles, we can analyze and determine the necessary horizontal forces to maintain equilibrium in fluid systems.**Note:** Ensure to substitute the known values and

Name: An inviscid fluid with density, ρ, discharges into the atmosphere thro
Uploaded: 2024-03-20T06:56:55.000Z
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Description: An inviscid fluid with density, ρ, discharges into the atmosphere through the device shown below. The height differences between the inlets and outlets are appreciable but unknown. Determine the horizontal component of force at the flange required to