HY8:Inlet Control Computations

Inlet control means that the amount of water the culvert barrel can carry is limited by the culvert entrance. Flow passes through critical depth at the culvert entrance and is supercritical in the barrel. There are several flow profiles possible, HY-8 simulates so-called Type A, B, C, and D conditions as shown below and as described in HDS-5. These profiles are known as Type 1 (A, B) and Type 5 (C, D) within HY-8 and are based on earlier work. The various flow type properties may be found in HY-8 by selecting the Flow Types button from the Culvert Summary Table and are shown below. Because the flow in the barrel is supercritical, outlet losses and friction losses are not reflected in the headwater elevation. The headwater elevation is a function of the entrance size, shape, and culvert type. The computed inlet control headwater elevation is found by accessing the results of scaled physical model tests. The logic for determining what inlet flow control type prevails is shown below (from the original HY-8 help file).

Inlet Control Logic

DETERMINE APPLICABLE INLET CONTROL EQUATION

1. IF circle or box with IMPROVED INLETS then use INLET equations.
2. For Straight (previously called conventional) INLETS

   A. If Q is < Q at .5D, then assume LOW FLOW INLET CONTROL:

   i. calculate CRITICAL DEPTH (DCO)

   ii. calculate Section Properties

   iii. VH = (Q / AC)^2 / 64.4

   iv. IH = DCO * LMULT + (1 + KELOW) * VH * VHCOEF

   IF no FALL THEN IHI = IH + I1E

   For Fall, HF = IH and check head on CREST.

   B. If Q > Q at .5D, but < Q at 3D, then use INLET REGRESSION EQUATIONS.

   C. If Q > Q at 3D, then assume HIGH FLOW INLET CONTROL.

   i. IH = (Q / CDAHI)^2 + .5 * RISE

   ii. IF no FALL THEN IHI = IH + I1E

   For Fall, HF = IH and check head on CREST.

INLET REGRESSION EQUATIONS (Q between Q at .5D and Q at 3D)

1. CIRCULAR

   A. See Straight inlet equations

   B. SIDE TAPERED ELLIPTICAL TRANSITION, THROAT CONTROL

   ZZ = Q / SQR(RISE ^ 5), Y = LOG(ZZ) / 2.30258

   i. IF n < .015 THEN SMOOTH PIPE IMPROVRD INLET.

   ii. If n >=.015 then ROUGH PIPE IMPROVED INLET.

   iii. Calculate THROAT CONTROL

   iv. Calculate FACE CONTROL

   v. IF FALL Then CW = CWF, calculate CREST control.

   C. SIDE TAPERED RECTANGULAR TRANSITION or SLOPE TAPERED

   i. Calculate THROAT CONTROL

   ii. Calculate FACE CONTROL

   iii. IF FALL Then CW = CWF, calculate CREST control.

2. BOX CULVERTS

   A. See Straight inlet equations

   B. SIDE TAPERED RECTANGULAR TRANSITION or SLOPE TAPERED

   i. Calculate THROAT CONTROL

   ii. Calculate FACE CONTROL

   iii. IF FALL Then CW = CWF, calculate CREST control.

3. PIPE ARCHES AND ELLIPSES

   A. See Straight inlet equations

4. IRREGULAR SHAPE

   A. See Straight inlet equations

Straight Inlet Equations

1. For IRREGULAR shape, X = Q / (AC * SQR(RISE))

   IF X <= .5 THEN IH = (A(1) * (X / .5)) * RISE

   ELSE IH = (A(J - 1) + (A(J) - A(J - 1)) * ((X - J + 2) / INC)) * RISE

2. For all others shapes, X = Q / (SPAN * SQR(RISE^3)): SR = SR(IC)

   IH = (A + (B + (C + (D + (E + F * X) * X) * X) * X) * X - SR * S0) * RISE

3. Headwater elevation (IHI) = IH + I1E if no fall.
4. For fall, CREST headwater is checked.

THROAT CONTROL TAPERED INLET

1. X = Q / (SPAN * SQR(RISE^3))
2. HT=RISE*(.1295033+(.3789944+(-.0437778+(4.26329E-03-1.06358E-04*X)*X)*X)*X)

FACE CONTROL-SIDE TAPERED INLET

1. ZZ = Q / (BF * SQR(RISE^3))
2. Calculate UNSUBMERGED: HF1 = (.56 * RISE) * (ZZ ^ .66667)
3. Calculate SUBMERGED

   A. For bevels: HF3 = (.0378 * (ZZ * ZZ) + .86) * RISE

   IF HF1 > RISE THEN HF = HF3

   IF HF1 < RISE THEN HF = HF1

   IF HF1 >= HF3 THEN HF = HF1

   B. For other edges: HF2 = (.0446 * (ZZ * ZZ) + .84) * RISE

   IF HF1 > RISE THEN HF = HF2

   IF HF1 < RISE THEN HF = HF1

   IF HF1 >= HF2 THEN HF = HF1

FACE CONTROL FOR SLOPE TAPERED INLET

1. ZZ = Q / (BF * SQR(RISE^3))
2. Calculate UNSUBMERGED: HF1 = (.5 * RISE) * (ZZ ^ .66667)

   A. For bevels: HF3 = (.0378 * (ZZ * ZZ) + .7) * RISE

   IF HF1 > RISE THEN HF = HF3

   IF HF1 < RISE THEN HF = HF1

   IF HF1 > HF3 THEN HF = HF1

   B. For other edges: HF2 = (.0446 * (ZZ * ZZ) + .64) * RISE

   IF HF1 > RISE THEN HF = HF2

   IF HF1 < RISE THEN HF = HF1

   IF HF1 > HF2 THEN HF = HF1

CREST CONTROL

1. HC = .5 * (Q / CW) ^ .66667

OUTLET CONTROL PROCEDURES THAT PRODUCE AN INLET CONTROL PROFILE

STEP

1. Compute critical depth (dco)
2. Compute normal depth (dno)
3. Compute fullflow if nomograph solution assumed "6-FFt or FFc".
4. If dno > .95(rise), assume fullflow "6-FFn".
5. If dno > dco, assume mild slope (SEE OUTLET.DAT).
6. If dno <= dco, assume steep slope.

   A. If twh is >= So(L) + rise, assume fullflow "4-FFt".\

   B. If twh is >= rise, outlet submerged, assume inlet unsubmerged.

   C. If twh is < rise, outlet is unsubmerged, assume inlet unsubmerged.

   i. Assume headwater (oh) = inlet control headwater (ih)

   Calculate S2 curve "1-S2n" for outlet depth.

   If oh >= rise, inlet submerged "5-S2n"

   ii. If twh > headwater, tailwater drowns out jump.

   Calculate M1 curve "3-M1t".

   If culvert flows part full, "7-Mit".

Inlet control means that the amount of water the culvert barrel can carry is limited by the culvert entrance. Flow passes through critical depth at the culvert entrance and is supercritical in the barrel. There are several flow profiles possible, HY-8 simulates so-called Type A, B, C, and D conditions as shown below and as described in HDS-5. These profiles are known as Type 1 (A, B) and Type 5 (C, D) within HY-8 and are based on earlier work. The various flow type properties may be found in HY-8 by selecting the Flow Types button from the Culvert Summary Table and are shown below. Because the flow in the barrel is supercritical, outlet losses and friction losses are not reflected in the headwater elevation. The headwater elevation is a function of the entrance size, shape, and culvert type. The computed inlet control headwater elevation is found by accessing the results of scaled physical model tests. The logic for determining what inlet flow control type prevails is shown below (from the original HY-8 help file).

Inlet Control Logic

DETERMINE APPLICABLE INLET CONTROL EQUATION

1. IF circle or box with IMPROVED INLETS then use INLET equations.
2. For Straight (previously called conventional) INLETS

   A. If Q is < Q at .5D, then assume LOW FLOW INLET CONTROL:

   i. calculate CRITICAL DEPTH (DCO)

   ii. calculate Section Properties

   iii. VH = (Q / AC)^2 / 64.4

   iv. IH = DCO * LMULT + (1 + KELOW) * VH * VHCOEF

   IF no FALL THEN IHI = IH + I1E

   For Fall, HF = IH and check head on CREST.

   B. If Q > Q at .5D, but < Q at 3D, then use INLET REGRESSION EQUATIONS.

   C. If Q > Q at 3D, then assume HIGH FLOW INLET CONTROL.

   i. IH = (Q / CDAHI)^2 + .5 * RISE

   ii. IF no FALL THEN IHI = IH + I1E

   For Fall, HF = IH and check head on CREST.

INLET REGRESSION EQUATIONS (Q between Q at .5D and Q at 3D)

1. CIRCULAR

   A. See Straight inlet equations

   B. SIDE TAPERED ELLIPTICAL TRANSITION, THROAT CONTROL

   ZZ = Q / SQR(RISE ^ 5), Y = LOG(ZZ) / 2.30258

   i. IF n < .015 THEN SMOOTH PIPE IMPROVRD INLET.

   ii. If n >=.015 then ROUGH PIPE IMPROVED INLET.

   iii. Calculate THROAT CONTROL

   iv. Calculate FACE CONTROL

   v. IF FALL Then CW = CWF, calculate CREST control.

   C. SIDE TAPERED RECTANGULAR TRANSITION or SLOPE TAPERED

   i. Calculate THROAT CONTROL

   ii. Calculate FACE CONTROL

   iii. IF FALL Then CW = CWF, calculate CREST control.

2. BOX CULVERTS

   A. See Straight inlet equations

   B. SIDE TAPERED RECTANGULAR TRANSITION or SLOPE TAPERED

   i. Calculate THROAT CONTROL

   ii. Calculate FACE CONTROL

   iii. IF FALL Then CW = CWF, calculate CREST control.

3. PIPE ARCHES AND ELLIPSES

   A. See Straight inlet equations

4. IRREGULAR SHAPE

   A. See Straight inlet equations

Straight Inlet Equations

1. For IRREGULAR shape, X = Q / (AC * SQR(RISE))

   IF X <= .5 THEN IH = (A(1) * (X / .5)) * RISE

   ELSE IH = (A(J - 1) + (A(J) - A(J - 1)) * ((X - J + 2) / INC)) * RISE

2. For all others shapes, X = Q / (SPAN * SQR(RISE^3)): SR = SR(IC)

   IH = (A + (B + (C + (D + (E + F * X) * X) * X) * X) * X - SR * S0) * RISE

3. Headwater elevation (IHI) = IH + I1E if no fall.
4. For fall, CREST headwater is checked.

THROAT CONTROL TAPERED INLET

1. X = Q / (SPAN * SQR(RISE^3))
2. HT=RISE*(.1295033+(.3789944+(-.0437778+(4.26329E-03-1.06358E-04*X)*X)*X)*X)

FACE CONTROL-SIDE TAPERED INLET

1. ZZ = Q / (BF * SQR(RISE^3))
2. Calculate UNSUBMERGED: HF1 = (.56 * RISE) * (ZZ ^ .66667)
3. Calculate SUBMERGED

   A. For bevels: HF3 = (.0378 * (ZZ * ZZ) + .86) * RISE

   IF HF1 > RISE THEN HF = HF3

   IF HF1 < RISE THEN HF = HF1

   IF HF1 >= HF3 THEN HF = HF1

   B. For other edges: HF2 = (.0446 * (ZZ * ZZ) + .84) * RISE

   IF HF1 > RISE THEN HF = HF2

   IF HF1 < RISE THEN HF = HF1

   IF HF1 >= HF2 THEN HF = HF1

FACE CONTROL FOR SLOPE TAPERED INLET

1. ZZ = Q / (BF * SQR(RISE^3))
2. Calculate UNSUBMERGED: HF1 = (.5 * RISE) * (ZZ ^ .66667)

   A. For bevels: HF3 = (.0378 * (ZZ * ZZ) + .7) * RISE

   IF HF1 > RISE THEN HF = HF3

   IF HF1 < RISE THEN HF = HF1

   IF HF1 > HF3 THEN HF = HF1

   B. For other edges: HF2 = (.0446 * (ZZ * ZZ) + .64) * RISE

   IF HF1 > RISE THEN HF = HF2

   IF HF1 < RISE THEN HF = HF1

   IF HF1 > HF2 THEN HF = HF1

CREST CONTROL

1. HC = .5 * (Q / CW) ^ .66667

OUTLET CONTROL PROCEDURES THAT PRODUCE AN INLET CONTROL PROFILE

STEP

1. Compute critical depth (dco)
2. Compute normal depth (dno)
3. Compute fullflow if nomograph solution assumed "6-FFt or FFc".
4. If dno > .95(rise), assume fullflow "6-FFn".
5. If dno > dco, assume mild slope (SEE OUTLET.DAT).
6. If dno <= dco, assume steep slope.

   A. If twh is >= So(L) + rise, assume fullflow "4-FFt".\

   B. If twh is >= rise, outlet submerged, assume inlet unsubmerged.

   C. If twh is < rise, outlet is unsubmerged, assume inlet unsubmerged.

   i. Assume headwater (oh) = inlet control headwater (ih)

   Calculate S2 curve "1-S2n" for outlet depth.

   If oh >= rise, inlet submerged "5-S2n"

   ii. If twh > headwater, tailwater drowns out jump.

   Calculate M1 curve "3-M1t".

   If culvert flows part full, "7-Mit".