All questions of Bernoulli’s Equation for EmSAT Achieve Exam

Bernoulli's theorem, in fluid dynamics, relation among the pressure, velocity, and elevation in a moving fluid (liquid or gas), the compressibility and viscosity (internal friction) of which are negligible and the flow of which is steady, or laminar.

True: Venturimeter is based on Bernoulli’s equation.

P' - P = (1/2)Xdensity of airX((V')^2_(V)^2)puting the values in the formula we get diff in pressure=4095

Bernoulli's principle can be derived from the principle of conservation of energy. This states that, in a steady flow, the sum of all forms of energy in a fluid along a streamline is the same at all points on that streamline.

Introduction:
The orifice meter is a type of flow meter used to measure the flow rate of fluid through a pipe. It consists of a flat rectangular plate with a small hole, known as an orifice, through which the fluid passes. This question is asking whether the given statement about the orifice meter is true or false.

Explanation:
The correct answer is option 'B', which states that the given statement is false. Let's understand why this is the correct answer.

Orifice Plate:
The orifice meter typically consists of a circular orifice plate rather than a flat rectangular plate. The orifice plate is installed perpendicular to the flow direction and creates a pressure difference across itself. This pressure difference is then used to determine the flow rate of the fluid.

Working Principle:
When the fluid passes through the orifice plate, it experiences a reduction in cross-sectional area, leading to an increase in fluid velocity. According to Bernoulli's principle, this increase in velocity corresponds to a decrease in pressure. The pressure difference across the orifice plate is measured using pressure taps located upstream and downstream of the plate.

Calculation of Flow Rate:
The flow rate through the orifice meter can be calculated using various equations, such as the Bernoulli equation, the continuity equation, and the discharge coefficient. These equations take into account the pressure difference, the properties of the fluid, and the dimensions of the orifice plate.

Advantages and Disadvantages:
The orifice meter has several advantages, including simplicity, low cost, and wide applicability. However, it also has limitations, such as pressure loss, sensitivity to changes in fluid properties, and the need for accurate calibration.

Conclusion:
In conclusion, the orifice meter used for measuring fluid flow does not consist of a flat rectangular plate. Instead, it employs a circular orifice plate. Therefore, the given statement is false.

False

Explanation:
In case of any orifice, the velocity does not always remain constant. The velocity of fluid flowing through an orifice depends on various factors such as the size of the orifice, the pressure difference across the orifice, and the properties of the fluid. Therefore, the discharge cannot be calculated solely based on the assumption that the velocity remains constant.

Factors affecting the velocity and discharge through an orifice:

1. Size of the orifice: The size of the orifice affects the velocity and discharge of the fluid. A smaller orifice will result in a higher velocity and discharge, while a larger orifice will result in a lower velocity and discharge.

2. Pressure difference across the orifice: The pressure difference across the orifice also affects the velocity and discharge. A higher pressure difference will result in a higher velocity and discharge, while a lower pressure difference will result in a lower velocity and discharge.

3. Properties of the fluid: The properties of the fluid, such as its density and viscosity, also play a role in determining the velocity and discharge. A more viscous fluid will have a lower velocity and discharge compared to a less viscous fluid.

Calculation of the discharge through an orifice:

The discharge through an orifice can be calculated using the following equation:

Q = Cd * A * √(2gh)

Where:
Q = Discharge
Cd = Coefficient of discharge
A = Area of the orifice
g = Acceleration due to gravity
h = Head difference across the orifice

The coefficient of discharge takes into account the various factors that affect the velocity and discharge, such as the shape of the orifice, the roughness of the edges, and the contraction and expansion of the flow. Therefore, it is necessary to consider these factors and use the appropriate value of the coefficient of discharge in the calculation.

Conclusion:

In conclusion, the velocity does not always remain constant in case of any orifice. The velocity and discharge through an orifice depend on various factors such as the size of the orifice, the pressure difference across the orifice, and the properties of the fluid. Therefore, it is important to consider these factors and use the appropriate equations, such as the discharge equation mentioned above, to calculate the discharge accurately.

Bernoulli’s Theorem
Bernoulli’s theorem, in fluid dynamics, relation among the pressure, velocity, and elevation in a moving fluid (liquid or gas), the compressibility and viscosity (internal friction) of which are negligible and the flow of which is steady, or laminar. First derived (1738) by the Swiss mathematician Daniel Bernoulli, the theorem states, in effect, that the total mechanical energy of the flowing fluid, comprising the energy associated with fluid pressure, the gravitational potential energy of elevation, and the kinetic energy of fluid motion, remains constant. Bernoulli’s theorem is the principle of energy conservation for ideal fluids in steady, or streamline, flow and is the basis for many engineering applications.

An orifice is typically called when referring to a small opening or hole, especially in a body or instrument, through which fluid or gas can pass.

Bernoulli's theorem. Bernoulli's theorem, in fluid dynamics, relation among the pressure, velocity, and elevation in a moving fluid (liquid or gas), the compressibility and viscosity (internal friction) of which are negligible and the flow of which is steady, or laminar.

The Bernoulli equation is an important expression relating pressure, height and velocity of a fluid at one point along its flow. Because the Bernoulli equation is equal to a constant at all points along a streamline, we can equate two points on a streamline.

Cheapest device for measuring flow/discharge rate

Orificemeter is the cheapest device for measuring flow/discharge rate among the given options.

Explanation

Orificemeter is a device used for measuring the flow of fluids. It consists of a flat plate with a hole in the center. When the fluid flows through the hole, its velocity increases and its pressure decreases. By measuring the pressure difference between the upstream and downstream sides of the plate, the flow rate can be calculated.

The cost of orificemeter is relatively low compared to other flow measuring devices like venturimeter and pitot tube. This is because orificemeter is a simple device with no moving parts and can be easily installed.

On the other hand, venturimeter and pitot tube are more complex devices with multiple components and require precise installation to accurately measure the flow. Therefore, these devices are more expensive than orificemeter.

Conclusion

In conclusion, orificemeter is the cheapest device for measuring flow/discharge rate among the given options. It is a simple and reliable device that can be easily installed and maintained.

The Bernoulli principle applies to any type of fluid, including liquids and gases.

The Bernoulli equation is an important expression relating pressure, height and velocity of a fluid at one point along its flow. Because the Bernoulli equation is equal to a constant at all points along a streamline, we can equate two points on a streamline.