Glycerine of density 1.25×10^3 " " kg/m^3 is flowing in conical shaped | PGMN Solutions

Glycerine of density 1.25×10^3 " " kg/m^3 is flowing in conical shaped horizontal pipe. Cross-sectional area of the pipe at its both ends is 10〖" " cm〗^2 and 5 cm^2 respectively. Pressure difference at both the ends is 10〖" " cm〗^2 and 5〖" " cm〗^2 respectively. Pressure difference at both the ends is 3" " N/m^2. Rate of flow of liquid in the pipe is
(A) 4×10^(-5) 〖" " m〗^3/s
(B) 2×10^(-5) 〖" " m〗^3/s
(C) 5×10^(-5) 〖" " m〗^3/s
(D) 6×10^(-5) 〖" " m〗^3/s



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🚀 Step-by-Step Solution to Solve This Question 🚀
📌 Chapter: Mechanical Properties of Fluids
📌 Topic: Fluid Flow through a Pipe

🔹 Step 1: In fluid dynamics, when a liquid flows through a pipe, the rate at which it flows (the flow rate) depends on the pressure difference, the cross-sectional area of the pipe, and the fluid's properties. The fluid’s velocity changes as it passes through regions of varying cross-sectional area.

🔹 Step 2: As the liquid moves from the larger to the smaller cross-sectional area of the pipe, its velocity increases because the same volume of fluid must pass through a smaller space in the same amount of time. This increase in velocity is accompanied by a decrease in pressure due to the relationship between pressure and velocity in fluid dynamics.

🔹 Step 3: The pressure difference between the two ends of the pipe helps push the fluid, causing it to accelerate. The rate at which the liquid flows is determined by both the pressure difference and the change in velocity at the two ends. Since the pipe has a varying cross-sectional area, this change in velocity also contributes to the overall flow rate.

🔹 Step 4: The rate of flow of liquid through the pipe can be found by considering the pressure difference, the density of the liquid, and the areas at both ends. The larger the pressure difference and the greater the difference in cross-sectional areas, the higher the flow rate.

✅ Final Answer: Option (A) 4×10⁻⁵ m³/s

🔥 Pro Tip: In problems involving fluid flow through pipes with varying cross-sectional areas, remember that the flow rate remains constant, but the velocity and pressure change based on the area. The pressure difference plays a key role in driving the flow.
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