Solve Vertical Venturi Meter Discharge w/ Mercury & Data

In summary, to calculate the discharge through the pipe, we need to use the Bernoulli equation and the continuity equation. We can use the Bernoulli equation to relate the pressure at two different points and the continuity equation to find the velocity at each point. Then, we can plug these values into the equations to solve for the discharge.
  • #1
saulabur
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Homework Statement


Considering that water flows in the pipe and mercury is used in the manometer, compute the discharge through the pipe. Please see the attached information for the given data.


Homework Equations



Bernoulli: (P1/rho * g) + (V1^2/2g) + Z1 = (P2/rho * g) + (V2^2/2g) + Z2

and Continuity: Q=v * A = v1 * A1 = v2 * A2

The Attempt at a Solution



Until now I have:
Z1=0, Z2=75cm

A1=707cm^2
A2=177cm^2

The problem is, that I don´t know how to measure the pressure by having the mercury (H=36cm)

Can anybody help me?
 

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  • #2




To calculate the discharge through the pipe, we need to use the Bernoulli equation and the continuity equation. The Bernoulli equation relates the pressure, velocity, and height of a fluid at two different points along a streamline. The continuity equation states that the volume flow rate is constant along a streamline.

In this case, we can use the Bernoulli equation to relate the pressure at the two points, P1 and P2. The height, Z1 and Z2, are already given in the problem. However, we need to find the velocity at each point in order to solve for the discharge.

To find the velocity, we can use the continuity equation. We know that the volume flow rate is constant, so we can set the two velocity values equal to each other and solve for V2.
V2 = (V1 * A1) / A2

Now that we have the velocity at point 2, we can plug it into the Bernoulli equation to solve for the pressure at point 2.
P2 = (P1 * A1/A2) + (V1^2/2g) - (V2^2/2g) - (rho * g * (Z2-Z1))

Once we have the pressure at point 2, we can use the continuity equation again to solve for the discharge, Q.
Q = V2 * A2

I hope this helps in finding the discharge through the pipe. Please let me know if you have any further questions.
 

What is a Vertical Venturi Meter?

A Vertical Venturi Meter is a type of flow meter used to measure the discharge of a fluid, typically water or air. It works by utilizing a constriction in the flow path, which causes a decrease in pressure. This decrease in pressure can then be correlated to the flow rate of the fluid.

Why use Mercury in a Vertical Venturi Meter?

Mercury is commonly used in Vertical Venturi Meters because of its high density and low vapor pressure. This makes it an ideal fluid for accurately measuring small flow rates. Additionally, mercury is non-corrosive and does not react with most other fluids, making it a reliable choice for scientific experiments.

How do you solve for discharge using a Vertical Venturi Meter with Mercury?

The discharge of a fluid can be calculated using the equation Q = √(2gΔhρ/ρm), where Q is the discharge, g is the acceleration due to gravity, Δh is the difference in height of the fluid levels, ρ is the density of the fluid being measured, and ρm is the density of mercury. This equation can be rearranged to solve for Q.

What data is needed to solve for discharge using a Vertical Venturi Meter with Mercury?

To solve for discharge using a Vertical Venturi Meter with Mercury, you will need to measure the difference in height of the fluid levels (Δh), the density of the fluid being measured (ρ), and the density of mercury (ρm). These values can then be plugged into the equation Q = √(2gΔhρ/ρm) to calculate the discharge.

What are some potential sources of error when using a Vertical Venturi Meter with Mercury?

Some potential sources of error when using a Vertical Venturi Meter with Mercury include measurement errors, such as inaccurate readings of the fluid levels or incorrect density values, and environmental factors, such as changes in temperature or atmospheric pressure. Additionally, any air bubbles present in the fluid can also affect the accuracy of the measurement. It is important to carefully control and account for these potential sources of error when using a Vertical Venturi Meter with Mercury.

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