Head At Entrance Given Discharge Through Channel Calculator

Formula Used:

\[ Loss\ of\ Head\ at\ Entrance = \left( \frac{Discharge\ of\ Channel}{Coefficient\ of\ Discharge \times Cross\ Section\ Area\ 1 \times Cross\ Section\ Area\ 2 \times \sqrt{\frac{2 \times [g]}{Cross\ Section\ Area\ 1^2 - Cross\ Section\ Area\ 2^2}}}} \right)^2 + Loss\ of\ Head\ at\ Exit \] \[ h_i = \left( \frac{Q}{C_d \times A_i \times A_f \times \sqrt{\frac{2 \times [g]}{A_i^2 - A_f^2}}}} \right)^2 + h_o \]

Discharge of Channel (Q):

m³/s

Coefficient of Discharge (C_d):

Cross Section Area 1 (A_i):

m²

Cross Section Area 2 (A_f):

m²

Loss of Head at Exit (h_o):

Head at Entrance (h_i):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Head at Entrance?

Head at Entrance refers to the energy loss that occurs when fluid flows from a larger reservoir into a channel or pipe. This loss is due to the contraction of flow and the formation of vena contracta at the entrance.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ h_i = \left( \frac{Q}{C_d \times A_i \times A_f \times \sqrt{\frac{2 \times [g]}{A_i^2 - A_f^2}}}} \right)^2 + h_o \]

Where:

\( h_i \) — Head at Entrance (m)
\( Q \) — Discharge of Channel (m³/s)
\( C_d \) — Coefficient of Discharge
\( A_i \) — Cross Section Area 1 (m²)
\( A_f \) — Cross Section Area 2 (m²)
\( [g] \) — Gravitational acceleration (9.80665 m/s²)
\( h_o \) — Loss of Head at Exit (m)

Explanation: The formula calculates the head loss at entrance based on discharge, cross-sectional areas, coefficient of discharge, and exit head loss.

3. Importance of Head Calculation

Details: Accurate head calculation is crucial for designing efficient fluid transport systems, determining energy losses, and ensuring proper system performance in hydraulic engineering applications.

4. Using the Calculator

Tips: Enter discharge in m³/s, coefficient of discharge (typically between 0.6-0.98), cross-sectional areas in m², and exit head loss in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for coefficient of discharge?
A: The coefficient of discharge typically ranges from 0.6 to 0.98, depending on the shape and smoothness of the entrance.

Q2: Why is head loss important in channel design?
A: Head loss affects the energy requirements, pumping costs, and overall efficiency of fluid transport systems.

Q3: What factors affect head loss at entrance?
A: Entrance geometry, flow velocity, fluid properties, and surface roughness are the main factors affecting head loss.

Q4: How can head loss be minimized?
A: Using well-rounded entrances, smooth transitions, and proper flow conditions can help minimize head loss.

Q5: Is this formula applicable to all fluids?
A: The formula is primarily designed for water and similar Newtonian fluids. For non-Newtonian fluids, additional considerations may be needed.