A Venturi flow meter is used to measure the the flow velocity of a water main. The water main has a diameter of 40.0 cm, and the constriction has a diameter of 10.0 cm. The two vertical pipes are open at the top, and the difference in water level between them is 2.0 m. Find the velocity, vm (in m/s), and the volumetric flow rate, Q (in m3/s), of the water in the main.
vm=
Q=
vm = 2.213594362
Q = 0.278168471
Hi, Unknown. Please show formula for your answer on Venturi flow meter. I would like to compare with mine. Thanks.
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To find the velocity, vm, of the water in the main using a Venturi flow meter, you can use Bernoulli's equation. Bernoulli's equation relates the pressure, density, and velocity of a fluid flowing through a pipe. Here's how you can solve for vm:
1. Start by determining the pressure difference (ΔP) between the two sections of the Venturi flow meter. This is given by the difference in water level between the two vertical pipes, which is 2.0 m. The pressure difference is then given by ΔP = ρ * g * h, where ρ is the density of water (normally around 1000 kg/m³), g is the acceleration due to gravity (9.8 m/s²), and h is the height difference (2.0 m).
2. Next, calculate the cross-sectional areas of the two sections. The area of the water main (A1) is given by A1 = π * (d1/2)², where d1 is the diameter of the water main (40.0 cm or 0.4 m). The area of the constriction (A2) is calculated similarly using the diameter of the constriction (10.0 cm or 0.1 m).
3. Now, using the mass conservation equation, we know that the volumetric flow rate, Q, is constant throughout the Venturi flow meter. Therefore, we can write A1 * v1 = A2 * v2, where v1 and v2 are the velocities in the water main and the constriction, respectively.
4. Since the flow is incompressible and the density of the fluid is constant, we can rewrite the above equation as v1 = (A2/A1) * v2.
5. Finally, substitute the values and solve for velocity vm: vm = (A2/A1) * sqrt(2 * ΔP/ρ), where sqrt represents the square root.
Now that we have vm, we can calculate the volumetric flow rate, Q:
6. Using the formula Q = A1 * vm, substitute the calculated value for vm and the known value for A1 to find Q.
So to summarize:
vm = (A2/A1) * sqrt(2 * ΔP/ρ)
Q = A1 * vm