γ [Increase from (1) to (2)] γ (1ft) [Decrease from (2) to (B)]

Transcription

1 1. The manometer fluid in the manometer of igure has a specific gravity of Pipes A and B both contain water. If the pressure in pipe A is decreased by 1.3 psi and the pressure in pipe B increases by 0.9 psi, determine the new differential reading of the manometer. Sol) Let s choose several points as shown and check the pressure change, (A) (1) () (B) (1) p A [at (A)] γ ( ft) [Increase from (A) to (1)] + water + g ( ft) water γ [Increase from (1) to ()] γ (1ft) [Decrease from () to (B)] p B [at (B)] () where γ g SG γ water ( 3.46) (6.4) lb/ft 3 Then, Pressure difference Δ p p B p A Δp p B pa ( 6.4)() + (3.46)(6.4)() (6.4)(1) lb/ft Equation (1) If the pressure in pipe A is decreased by 1.3 psi and the pressure in pipe B increases by 0.9 psi, then Point (1): Move upward by Δ h1 Point (): Move downward by Δ h Δp ' ( pb psi) ( pa 1.3 psi) ( pb pa) +. psi ( 6.4)( Δh1 ) + (3.46)(6.4)[ + ( Δh1 + Δh ) (6.4)(1 + Δh ) [( 6.4)(1) + (3.46)(6.4)()] + (6.4)[(3.46) 1]( Δh1 + Δh ) [rom eq. (1)] Then, lb in. (1 ) Δh in ft 1 + Δh.06 ft lb (6.4 )(.46) 3 ft New differential reading ft + Δh + Δh ft (Answer) 1

2 . Determine the elevation difference, between the water levels in the two open tanks shown. Sol) Let s choose several points as shown and check the pressure change, (1) () (3) (4) p 1 [At (1)] γ water l [Decrease from (1) to ()] + γ g (0.4 m) [Increase from () to (3)] + γ water ( l Δh) [Increase from (3) to (4)] p ) [at (4)] (Atmospheric pressure) 4 ( p1 where p 1 p4 0 (The atmosphere) γ g SG γ water ( 0.9) (9800) N/m 3 Unknown l : Disappear during calculation 1 Then, Δh (0.4γ )(1 0.9) m (Answer) γ (1) l () (3) (4)

3 3. A 3-m wide, 8-m high rectangular gate is located at the end of a rectangular passage that is connected to a large open tank filled with water as shown in ig. The gate is hinged at its bottom and held closed by a horizontal force, H. The water depth (h) above the center of the gate is 16 m. 16 m Specific weight of water kn γ m (a) Determine the hydrostatic force on the gate ( R ) and the position of hydrostatic force ( y R ). (Note. Use the moment of inertia of the area as below.) (b) Determine the Moment (or Torque) developed by R about the axis passing through the bottom hinge. (c) Using the results from Questions (a) and (b), determine the required horizontal force, H in order to keep the gate closed. Sol) (a) R γhc A (Pressure at the center of the gate) (Area of the gate) where h 16 m & A m c R γ hc A ( 9.8)(16)(4) 3760 kn (ANSWER) In addition, the position of R ( y R ) I xc yr yc + where y c h c 16 m & 1 1 I (height) (4) (8) xc A 18 m 4 y A 1 1 c I xc 18 yr yc m (ANSWER) y A 16 4 (b) Moment developed by c R M ( 0 y ) kn m R R R (c) To keep the gate closed, Moment developed by R Moment due to Horizontal force, H i.e. M hinge R ( 0 yr ) H (4) 0 H 3450 kn (ANSWER) 4

4 4. A 4-m-long curved gate is located in the side of a reservoir containing water as shown. Determine the magnitude of the horizontal and vertical components of the force of the water on the gate. Will this force pass through point A? Explain. h R Step 1. Consider a volume of fluids shown and ind all forces acting on the gate Draw a free-body diagram as shown 1 W - R a) Horizontal component H 1 1 γhc1 A1 (9800)(7.5)(4 3) 88000N or 88 kn where h c1 Depth of the center of vertical area A 1 Vertical area b) Vertical component V + W h A (9800)(6)(4 3) γ c N or kn 1 1 W γ ( Volume) γ[ π ( r) ( D)] (9800)[ π (3) (4)] N or 76.9 kn kN and kn (Answer) H r R V r r H + V [Pressure force R acting on a point on the wall : Perpendicular to the surface : Parallel to the radius of curvature of the wall : Pass the center of radius of the curvature, A]

5 5. The homogeneous wooden block A of figure is 0.7 m 0.7 m 1.3 m and weighs.4 kn. The concrete block B (specific weight 3.6 kn/m 3 ) is suspended from A by means of the slender cable causing A to float in the position indicated. Determine the volume of B. Sol) or equilibrium, all vertical forces should be balanced, i.e. vertical 0 So that T W for a wooden block (see figure) B W where γ ( submerged volume) B water 3 1 (9.80 kn/m ) (1.3 m 0.7 m 0.7 m) 3.1 kn B T T Thus, T B W kn W C Then, for a concrete block, BC BC W C T where γ V ) and W γ V ) BC water ( C C concrete ( C or, γ ( V ) γ ( V ) 0. 7 water C concrete C 0.7 kn 0.7 Then, V C γ γ 3.6 kn/m 9.80 kn/m concrete water m 3 (Answer)

6 6. An open rectangular tank 1 m wide and m long contains gasoline to a depth of 1 m. If the height of the tank sides is 1.5 m, what is the maximum horizontal acceleration (along the long axis of the tank) that can develop before the gasoline would begin to spill? Sol) rom the equation for the line of constant pressure, a y dz dy a a y where z 0 g + az In order to prevent spilling, dz dy : Slope of the line of constant pressure (see figure) 1.5 m.0 m z 1.0 m y So that dz a y g ( 0.5) g dy inally, ( ) ( 0.5)(9.81) a m/s (Answer) y max